EDA for Gas Fees - V2

In this notebook we perform Exploratory Data Analysis (EDA) on FIL's gas fee mechanism. The goal is to observe the gas fee as a signal and attempt to understand what may be driving it.

Questions to be answered in this notebook:

• Understand data we have by performing a data baseline - event and aggregated data.
• Reverse engineer June 3 spike - what happened and why? Can we generalize what drives burning?
• Distribution of attributes of things people are willing to pay gas fees for. What types of transactions are individuals paying more for?
• Reperform Granger Causality when we have more data understanding

Potential steps:

• Are revenues over cost?
• Obtain message metadata, try and predict cost from it (classifier or regressor). Which attributes are mapped to smaller or larger costs? Which messages are worth paying a lot for? The question is what people are they paying for and why?

Change log:

Background information: What are Gas Fees?

Note: this description is copied from the official Filecoin documentation

Executing messages, for example by including transactions or proofs in the chain, consumes both computation and storage resources on the network. Gas is a measure of resources consumed by messages. The gas consumed by a message directly affects the cost that the sender has to pay for it to be included in a new block by a miner.

Historically in other blockchains, miners specify a GasFee in a unit of native currency and then pay the block producing miners a priority fee based on how much gas is consumed by the message. Filecoin works similarly, except an amount of the fees is burned (sent to an irrecoverable address) to compensate for the network expenditure of resources, since all nodes need to validate the messages. The idea is based on Ethereum's EIP1559.

The amount of fees burned in the Filecoin network comes given by a dynamic BaseFee which gets automatically adjusted according to the network congestion parameters (block sizes). The current value can be obtained from one of the block explorers or by inspecting the current head.

Additionally, a number of gas-related parameters are attached to each message and determine the amount of rewards that miners get. Here's an overview of the terms and concepts:

GasUsage: the amount of gas that a message's execution actually consumes. Current protocol does not know how much gas a message will exactly consume ahead of execution, but it can be estimated (see prices (opens new window)). GasUsage measured in units of Gas.

BaseFee: the amount of FIL that gets burned per unit of gas consumed for the execution of every message. It is measured in units of attoFIL/Gas.

GasLimit: the limit on the amount of gas that a message's execution can consume, estimated and specified by a message sender. It is measured in units of Gas. The sum of GasLimit for all messages included in a block must not exceed the BlockGasLimit. Messages will fail to execute if they run out of Gas, and any effects of the execution will be reverted.

GasFeeCap: the maximum token amount that a sender is willing to pay per GasUnit for including a message in a block. It is measured in units of attoFIL/Gas. A message sender must have a minimum balance of GasFeeCap * GasLimit when sending a message, even though not all of that will be consumed. GasFeeCap can serve as a safeguard against high, unexpected BaseFee fluctuations.

GasPremium: a priority fee that is paid to the block-producing miner. This is capped by GasFeeCap. The BaseFee has a higher priority. It is measured in units of attoFIL/Gas and can be as low as 1 attoFIL/Gas.

Overestimation burn: an additional amount of gas to burn that grows larger when the difference between GasLimit and GasUsage is large.

The total cost of a message for a sender will be:

• GasUsage * BaseFee FIL (burned) +
• GasLimit * GasPremium FIL (miner's reward) +
• OverEstimationBurn * BaseFee FIL

An important detail is that a message will always pay the burn fee, regardless of the GasFeeCap used. Thus, a low GasFeeCap may result in a reduced GasPremium or even a negative one! In that case, the miners that include a message will have to pay the needed amounts out of their own pockets, which means they are unlikely to include such messages in new blocks.

Filecoin implementations may choose the heuristics of how their miners select messages for inclusion in new blocks, but they will usually attempt to maximize the miner's rewards.

Data Resources

• https://hackmd.io/5leND7tITX--5NJsFCJyow # Existing Sentinel queries
• https://github.com/filecoin-project/sentinel/blob/master/docs/sentinel_tables_purpose.csv # Sentinel Tables Purpose

Sentinel Diagram

# import libraries
from sqlalchemy import create_engine
import pandas as pd
from datetime import datetime
from statsmodels.tsa.api import VAR
from sklearn.preprocessing import StandardScaler
from statsmodels.tsa.stattools import adfuller
from math import sqrt
import matplotlib.pyplot as plt
import seaborn as sns
import scipy.stats as stats
import numpy as np
import seaborn as sns


from Cryptoeconomics_signal_processing import time_analysis, fourier_transform, phase_shift_overlay

%matplotlib inline

# load connection string
CONN_STRING_PATH = '../config/sentinel_conn_string_andrew.txt'


with open(CONN_STRING_PATH, 'r') as fid:
    conn_string = fid.read()
    
# create database connection.
connection = create_engine(conn_string, pool_recycle=3600).connect()

Data EDA

Below we download hourly averages from the messages and mesage_gas_economy table from May 1st, 2021 to present (last refreshed 6/28/2021). After downloading the data, we few the first and lasts 5 rows, and perform basic statistics on the data.

Data Dictionary - coped from Sentinel's Data Dictionary

derived_gas_outputs

Derived gas costs resulting from execution of a message in the VM.

Name	Type	Nullable	Description
actor_name	text	NO	Human readable identifier for the type of the actor.
base_fee_burn	text	NO	The amount of FIL (in attoFIL) to burn as a result of the base fee. It is parent_base_fee (or gas_fee_cap if smaller) multiplied by gas_used. Note: successfull window PoSt messages are not charged this burn.
cid	text	NO	CID of the message.
exit_code	bigint	NO	The exit code that was returned as a result of executing the message. Exit code 0 indicates success. Codes 0-15 are reserved for use by the runtime. Codes 16-31 are common codes shared by different actors. Codes 32+ are actor specific.
from	text	NO	Address of actor that sent the message.
gas_burned	bigint	NO	The overestimated units of gas to burn. It is a portion of the difference between gas_limit and gas_used.
gas_fee_cap	text	NO	The maximum price that the message sender is willing to pay per unit of gas.
gas_limit	bigint	YES	A hard limit on the amount of gas (i.e., number of units of gas) that a message’s execution should be allowed to consume on chain. It is measured in units of gas.
gas_premium	text	NO	The price per unit of gas (measured in attoFIL/gas) that the message sender is willing to pay (on top of the BaseFee) to "tip" the miner that will include this message in a block.
gas_refund	bigint	NO	The overestimated units of gas to refund. It is a portion of the difference between gas_limit and gas_used.
gas_used	bigint	NO	A measure of the amount of resources (or units of gas) consumed, in order to execute a message.
height	bigint	NO	Epoch this message was executed at.
method	bigint	YES	The method number to invoke. Only unique to the actor the method is being invoked on. A method number of 0 is a plain token transfer - no method exectution.
miner_penalty	text	NO	Any penalty fees (in attoFIL) the miner incured while executing the message.
miner_tip	text	NO	The amount of FIL (in attoFIL) the miner receives for executing the message. Typically it is gas_premium * gas_limit but may be lower if the total fees exceed the gas_fee_cap.
nonce	bigint	YES	The message nonce, which protects against duplicate messages and multiple messages with the same values.
over_estimation_burn	text	NO	The fee to pay (in attoFIL) for overestimating the gas used to execute a message. The overestimated gas to burn (gas_burned) is a portion of the difference between gas_limit and gas_used. The over_estimation_burn value is gas_burned * parent_base_fee.
parent_base_fee	text	NO	The set price per unit of gas (measured in attoFIL/gas unit) to be burned (sent to an unrecoverable address) for every message execution.
refund	text	NO	The amount of FIL (in attoFIL) to refund to the message sender after base fee, miner tip and overestimation amounts have been deducted.
size_bytes	bigint	YES	Size in bytes of the serialized message.
state_root	text	NO	CID of the parent state root.
to	text	NO	Address of actor that received the message.
value	text	NO	The FIL value transferred (attoFIL) to the message receiver.

message_gas_economy

Gas economics for all messages in all blocks at each epoch.

Name	Type	Nullable	Description
base_fee	double precision	NO	The set price per unit of gas (measured in attoFIL/gas unit) to be burned (sent to an unrecoverable address) for every message execution.
base_fee_change_log	double precision	NO	The logarithm of the change between new and old base fee.
gas_capacity_ratio	double precision	YES	The gas_limit_unique_total / target gas limit total for all blocks.
gas_fill_ratio	double precision	YES	The gas_limit_total / target gas limit total for all blocks.
gas_limit_total	bigint	NO	The sum of all the gas limits.
gas_limit_unique_total	bigint	YES	The sum of all the gas limits of unique messages.
gas_waste_ratio	double precision	YES	(gas_limit_total - gas_limit_unique_total) / target gas limit total for all blocks.
height	bigint	NO	Epoch these economics apply to.
state_root	text	NO	CID of the parent state root at this epoch.

messages

Validated on-chain messages by their CID and their metadata.

Name	Type	Nullable	Description
cid	text	NO	CID of the message.
from	text	NO	Address of the actor that sent the message.
gas_fee_cap	text	NO	The maximum price that the message sender is willing to pay per unit of gas.
gas_limit	bigint	NO	-
gas_premium	text	NO	The price per unit of gas (measured in attoFIL/gas) that the message sender is willing to pay (on top of the BaseFee) to "tip" the miner that will include this message in a block.
height	bigint	NO	Epoch this message was executed at.
method	bigint	YES	The method number invoked on the recipient actor. Only unique to the actor the method is being invoked on. A method number of 0 is a plain token transfer - no method exectution.
nonce	bigint	NO	The message nonce, which protects against duplicate messages and multiple messages with the same values.
size_bytes	bigint	NO	Size of the serialized message in bytes.
to	text	NO	Address of the actor that received the message.
value	text	NO	Amount of FIL (in attoFIL) transferred by this message.

We will focus on analyzing the methods by actor type using the derived gas outputs table. The data is very large, so we will perform individul SQL queries in order to obtain all of the required data.

# # message level data
QUERY = """
SELECT  
to_timestamp(height_to_unix(d.height)) AS timestamp,
d.actor_name,
d.base_fee_burn,
d.cid,
d.exit_code,
d.from,
d.gas_burned,
d.gas_fee_cap,
d.gas_limit,
d.gas_premium,
d.gas_refund,
d.gas_used,
d.height,
d.method,
d.miner_penalty,
d.miner_tip,
d.nonce,
d.over_estimation_burn,
d.parent_base_fee,
d.refund,
d.size_bytes,
d.state_root,
d.to,
d.value
FROM derived_gas_outputs d
WHERE
to_timestamp(height_to_unix(d.height)) BETWEEN '2021-06-01' AND '2021-06-02'
"""
derived_gas_outputs_message_level = (pd.read_sql(QUERY, connection))

For June 1 and June 2, what are the number of transactions by actor type?

derived_gas_outputs_message_level.actor_name.value_counts()

fil/4/storageminer      1481249
fil/4/account             30867
fil/4/storagemarket        2468
fil/4/multisig             1447
<unknown>                   106
fil/4/storagepower          105
fil/4/paymentchannel         13
Name: actor_name, dtype: int64

# # message level data
QUERY = """
SELECT DISTINCT
d.actor_name,
d.method
FROM derived_gas_outputs d
WHERE
to_timestamp(height_to_unix(d.height)) BETWEEN '2021-06-01' AND '2021-06-30'
GROUP BY
d.actor_name,
d.method
"""
derived_gas_outputs_message_level_actors = (pd.read_sql(QUERY, connection))

Count of all actor types and methods used during June.

derived_gas_outputs_message_level_actors

	actor_name	method
0	fil/4/account	0
1	fil/4/account	2
2	fil/4/account	3
3	fil/4/account	5
4	fil/4/init	2
5	fil/4/multisig	0
6	fil/4/multisig	2
7	fil/4/multisig	3
8	fil/4/paymentchannel	0
9	fil/4/storagemarket	2
10	fil/4/storagemarket	3
11	fil/4/storagemarket	4
12	fil/4/storageminer	0
13	fil/4/storageminer	3
14	fil/4/storageminer	4
15	fil/4/storageminer	5
16	fil/4/storageminer	6
17	fil/4/storageminer	7
18	fil/4/storageminer	8
19	fil/4/storageminer	9
20	fil/4/storageminer	10
21	fil/4/storageminer	11
22	fil/4/storageminer	15
23	fil/4/storageminer	16
24	fil/4/storageminer	18
25	fil/4/storageminer	20
26	fil/4/storageminer	21
27	fil/4/storageminer	22
28	fil/4/storageminer	23
29	fil/4/storageminer	24
30	fil/4/storagepower	2
31	fil/4/verifiedregistry	4
32	<unknown>	0
33	<unknown>	1

# # message level data
QUERY = """
SELECT 
d.base_fee_burn,
d.exit_code,
d.gas_burned,
d.gas_fee_cap,
d.gas_limit,
d.gas_premium,
d.gas_refund,
d.gas_used,
d.height,
d.method,
d.miner_penalty,
d.miner_tip,
d.nonce,
d.over_estimation_burn,
d.parent_base_fee,
d.refund
FROM derived_gas_outputs d
WHERE
to_timestamp(height_to_unix(d.height)) BETWEEN '2021-06-01' AND '2021-06-30'
AND d.actor_name = 'fil/4/storagemarket'
"""

derived_gas_outputs_message_level_storage_market = (pd.read_sql(QUERY, connection))

derived_gas_outputs_message_level_storage_market.describe()

	base_fee_burn	exit_code	gas_burned	gas_fee_cap	gas_limit	gas_premium	gas_refund	gas_used	height	method	miner_penalty	miner_tip	nonce	over_estimation_burn	parent_base_fee	refund
count	6.162100e+04	61621.000000	6.162100e+04	6.162100e+04	6.162100e+04	6.162100e+04	6.162100e+04	6.162100e+04	61621.000000	61621.000000	6.162100e+04	6.162100e+04	6.162100e+04	6.162100e+04	6.162100e+04	6.162100e+04
mean	4.077972e+16	0.010029	3.149639e+06	4.907266e+09	9.461527e+07	5.401222e+05	1.593134e+07	7.553429e+07	846308.565603	2.701660	3.712199e+10	5.211299e+13	4.294501e+04	1.772818e+15	5.151027e+08	3.931660e+17
std	8.308884e+16	0.407687	3.708446e+07	5.702000e+09	1.364981e+08	3.220969e+07	2.230157e+07	1.049736e+08	23904.654520	0.954238	8.437992e+12	5.624881e+15	1.095876e+05	3.217716e+16	5.082366e+08	6.334691e+17
min	1.060004e+09	0.000000	0.000000e+00	9.923600e+04	4.990251e+06	9.785700e+04	0.000000e+00	3.164190e+05	806640.000000	2.000000	0.000000e+00	0.000000e+00	0.000000e+00	0.000000e+00	1.000000e+02	0.000000e+00
25%	1.610871e+15	0.000000	3.749990e+05	8.400163e+08	1.342555e+07	9.990800e+04	2.248854e+06	1.080154e+07	825870.000000	2.000000	0.000000e+00	1.354255e+12	1.164900e+04	5.657481e+13	8.416376e+07	1.751587e+16
50%	7.358929e+15	0.000000	3.800620e+05	4.844441e+09	1.359130e+07	1.004860e+05	2.277422e+06	1.093414e+07	844469.000000	2.000000	0.000000e+00	3.530529e+12	3.041800e+04	2.530612e+14	4.118912e+08	7.686502e+16
75%	2.545670e+16	0.000000	4.481954e+06	6.277822e+09	1.513857e+08	2.040790e+05	2.570593e+07	1.189982e+08	866511.000000	4.000000	0.000000e+00	2.670426e+13	3.466600e+04	8.453336e+14	8.856992e+08	2.828606e+17
max	1.505270e+18	19.000000	8.749464e+09	1.898583e+11	9.021040e+09	5.032031e+09	1.244673e+08	5.589476e+08	890160.000000	4.000000	2.084783e+15	1.358518e+18	2.454082e+06	7.594399e+18	6.273926e+09	6.907386e+18

# derived_gas_outputs_message_level_storage_market.plot(x='height',y='gas_used',c='method',kind='scatter')

derived_gas_outputs_message_level_storage_market.hist(column='gas_used',by='method')
plt.title('Distributions of Storage Market Gased used by method')

Text(0.5, 1.0, 'Distributions of Storage Market Gased used by method')

QUERY = """
SELECT 
to_timestamp(height_to_unix(g.height)) as timestamp,
g.base_fee,
g.base_fee_change_log,
g.gas_capacity_ratio,
g.gas_fill_ratio,
g.gas_limit_total,
g.gas_limit_unique_total,
g.gas_waste_ratio
FROM message_gas_economy g
WHERE
to_timestamp(height_to_unix(g.height)) BETWEEN '2021-06-02' AND '2021-06-05'
ORDER BY
timestamp ASC
"""
message_gas_economy = (pd.read_sql(QUERY, connection))

# Use state root and parent state root to combine, height if not available

message_gas_economy.head()

	timestamp	base_fee	base_fee_change_log	gas_capacity_ratio	gas_fill_ratio	gas_limit_total	gas_limit_unique_total	gas_waste_ratio
0	2021-06-02 00:00:00+00:00	2.600000e-16	-0.257298	0.764315	1.998053	5.994159e+10	2.292944e+10	1.233738
1	2021-06-02 00:00:30+00:00	2.490000e-16	-0.367020	0.678527	1.988991	5.966973e+10	2.035580e+10	1.310464
2	2021-06-02 00:01:00+00:00	2.520000e-16	0.101680	1.113587	1.999106	3.998213e+10	2.227174e+10	0.885519
3	2021-06-02 00:01:30+00:00	2.630000e-16	0.362743	1.351031	1.999886	2.999829e+10	2.026547e+10	0.648855
4	2021-06-02 00:02:00+00:00	2.540000e-16	-0.295626	0.739098	1.995247	6.983364e+10	2.586842e+10	1.256149

QUERY = """
SELECT 
to_timestamp(height_to_unix(m.height)) as timestamp,
m.from,
m.gas_fee_cap,
m.method,
m.to
FROM messages m
WHERE
to_timestamp(height_to_unix(m.height)) BETWEEN '2021-06-02' AND '2021-06-05'
"""
messages = (pd.read_sql(QUERY, connection))

Time Analysis

When examining the data, we developed the following two questions:

1. Is the distribution of intervals between data points consistent?
2. What type of samplimg time do we have?

Workflow:

1. Verify sampling intervals
2. Verify distributions. If not normal, poisson, etc

To answer these questions, we will calculate the timestamp difference and create a histogram of the time differences and determine if we have equal time sampling or not.

messages['time'] = messages['timestamp'].apply(lambda x: x.value)

time_analysis(messages,'time')

Analyze Message meta data

messages.describe()

	gas_fee_cap	method	time	timestampDiff
count	4.644615e+06	4.644615e+06	4.644615e+06	4.644615e+06
mean	7.670292e+09	6.318362e+00	1.622721e+18	2.240659e+07
std	8.734661e+10	1.078328e+00	7.637262e+13	3.439053e+11
min	1.000000e+02	0.000000e+00	1.622592e+18	-1.738800e+14
25%	9.399679e+06	6.000000e+00	1.622653e+18	0.000000e+00
50%	1.926023e+09	6.000000e+00	1.622722e+18	0.000000e+00
75%	5.000000e+09	7.000000e+00	1.622788e+18	0.000000e+00
max	1.170783e+14	2.300000e+01	1.622851e+18	1.738800e+14

messages['method'].value_counts()

6     2197377
7     2173655
5      170165
0       85902
2       10074
11       3792
4        1653
16       1402
3         337
9         136
23         58
20         28
18         17
21         14
8           4
22          1
Name: method, dtype: int64

Required Mapping to unblock Message Analysis

• Method ID:
  • Input for methods. What is required, what isn't.
  • Output methods. What events does the method cause
• Actor type ID:
  • Description
  • Which methods actor type can use

Data is method id crossed with actor id. We don't know what they respresent. We need to blow out to understand, this is overly flat. Need two separate keys, one for method, one for actor.

Below is currently all we have to go on:

https://github.com/filecoin-project/specs-actors/tree/master/actors/builtin

https://github.com/filecoin-project/specs-actors/blob/master/actors/builtin/multisig/multisig_actor.go#L52-L64

messages['method'].hist()

<AxesSubplot:>

If this lookup table is correct, the vast majority of transactions are 6,7 and 5; which are RemoveSigner, SwapSigner, and AddSigner, respectively.

messages['from'].value_counts()

f3qcmmkbobbp6ed4psyvny6zsia5v32dlxnvpfgxsvpjtaptjyuapmd3i5zr2353fqe7a2kowceis65iyjzsoq    88709
f3vqd3cenprn6xdt73igrjukq5a7nh5rgjgajw5iev6snhv76o2sqmlgzbvq4vyje5ulrjriicsln6tz3xgimq    68142
f3ucq7fmnfoa3jsum7qjoeyz2gflwdcq4g44eiojll6lnlqe7wbx24tjvg5v4zfniwjk6cuo2l3mceq2we6kea    63760
f3sfemh6sz2zkrei23ra4fng4kjqr5tek4bleyxbrvcyndxvutmep27orixnjunm5cwqq25x4xlbup3jqbt3ua    52469
f3q2crv5dhkobq7y7fzgmfot7dtxbwe26r6wzp7ny43f5233tdzvzabdup2knjc46g6ogfi5zesn34byxhjaha    51858
                                                                                          ...  
f1etek4anvon2oby5smufuwy6ptlab3bva4pprpwi                                                     1
f1sn2xg6yil5cht3pyftbgkxb7khz7bvhvozkzzri                                                     1
f14ll6y5xuhdkddzzzjnxwoeghzxj5qteykb5nsda                                                     1
f1zlba45ayd4d5gyyhw3jbw5tqpfwjbl7u25ucfrq                                                     1
f1bwhjiifl77szahorzvigsqxano4t53dlszddevq                                                     1
Name: from, Length: 33612, dtype: int64

messages['to'].value_counts()

f0755327                                     88856
f0764901                                     88802
f0688165                                     74596
f0463143                                     68439
f0724216                                     66924
                                             ...  
f1o4vuaoekmcimfshxpzieln2vg6zuog74fbwn5wi        1
f17ijzaycegynkvttqvwjwwrcfn5h4bvy22tzljha        1
f1r6ju4dm7563a3hrqfd2oqvnce7sycyd3sy35yti        1
f13q7ecgqj32dyrggup74x5i4brirsxexfujyo2ai        1
f1zidvendbbjpp42exjfigdqfzdrzgkvjkxgxut5i        1
Name: to, Length: 37333, dtype: int64

messages['gas_fee_cap'] = messages['gas_fee_cap'].astype(float)
messages.plot(x='timestamp',y='gas_fee_cap')

<AxesSubplot:xlabel='timestamp'>

We will continue to focus on the derived_gas_outputs table with SQL queries to understand the why behind transactions as we do not have actor information easily accessible from the messages table.

Analyze message gas economy data

message_gas_economy.describe()

	base_fee	base_fee_change_log	gas_capacity_ratio	gas_fill_ratio	gas_limit_total	gas_limit_unique_total	gas_waste_ratio
count	8.580000e+03	8580.000000	8580.000000	8580.000000	8.580000e+03	8.580000e+03	8580.000000
mean	1.474750e-10	0.000378	1.008772	1.966365	4.784484e+10	2.117030e+10	0.957592
std	2.446596e-10	0.386090	0.372284	0.080264	2.162609e+10	5.598819e+09	0.366611
min	1.000000e-16	-0.827117	0.257397	0.526751	3.227862e+09	3.227862e+09	0.000000
25%	9.066125e-14	-0.285272	0.733050	1.975605	2.994499e+10	1.774505e+10	0.758082
50%	1.523809e-11	-0.057982	0.941155	1.988402	4.886860e+10	2.093772e+10	1.022318
75%	2.322379e-10	0.219020	1.212218	1.994668	5.976858e+10	2.428649e+10	1.227833
max	1.961212e-09	1.000000	2.000000	2.000000	1.392380e+11	6.030551e+10	1.719983

message_gas_economy, decomposed_base_fee = fourier_transform(message_gas_economy,'base_fee',10)

Fourier Transform of base_fee with 10 components.

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

message_gas_economy, decomposed_base_fee_change_log = fourier_transform(message_gas_economy,'base_fee_change_log',10)

Fourier Transform of base_fee_change_log with 10 components.

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

message_gas_economy, decomposed_gas_capacity_ratio = fourier_transform(message_gas_economy,'gas_capacity_ratio',10)

Fourier Transform of gas_capacity_ratio with 10 components.

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

message_gas_economy, decomposed_gas_fill_ratio = fourier_transform(message_gas_economy,'gas_fill_ratio',10)

Fourier Transform of gas_fill_ratio with 10 components.

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

message_gas_economy, decomposed_gas_limit_total = fourier_transform(message_gas_economy,'gas_limit_total',10)

Fourier Transform of gas_limit_total with 10 components.

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

message_gas_economy, decomposed_gas_limit_unique_total = fourier_transform(message_gas_economy,'gas_limit_unique_total',10)

Fourier Transform of gas_limit_unique_total with 10 components.

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

message_gas_economy, decomposed_gas_waste_ratio = fourier_transform(message_gas_economy,'gas_waste_ratio',10)

Fourier Transform of gas_waste_ratio with 10 components.

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

/opt/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

Exogenous signals

https://github.com/filecoin-project/sentinel/blob/master/docs/db.md

chain_economics

Economic summaries per state root CID.

Name	Type	Nullable	Description
burnt_fil	text	NO	Total FIL (attoFIL) burned as part of penalties and on-chain computations.
circulating_fil	text	NO	The amount of FIL (attoFIL) circulating and tradeable in the economy. The basis for Market Cap calculations.
locked_fil	text	NO	The amount of FIL (attoFIL) locked as part of mining, deals, and other mechanisms.
mined_fil	text	NO	The amount of FIL (attoFIL) that has been mined by storage miners.
parent_state_root	text	NO	CID of the parent state root.
vested_fil	text	NO	Total amount of FIL (attoFIL) that is vested from genesis allocation.

chain_powers

Power summaries from the Power actor.

Name	Type	Nullable	Description
height	bigint	NO	Epoch this power summary applies to.
miner_count	bigint	YES	Total number of miners.
participating_miner_count	bigint	YES	Total number of miners with power above the minimum miner threshold.
qa_smoothed_position_estimate	text	NO	Total power smoothed position estimate - Alpha Beta Filter "position" (value) estimate in Q.128 format.
qa_smoothed_velocity_estimate	text	NO	Total power smoothed velocity estimate - Alpha Beta Filter "velocity" (rate of change of value) estimate in Q.128 format.
state_root	text	NO	CID of the parent state root.
total_pledge_collateral	text	NO	Total locked FIL (attoFIL) miners have pledged as collateral in order to participate in the economy.
total_qa_bytes_committed	text	NO	Total provably committed, quality adjusted storage power in bytes. Quality adjusted power is a weighted average of the quality of its space and it is based on the size, duration and quality of its deals.
total_qa_bytes_power	text	NO	Total quality adjusted storage power in bytes in the network. Quality adjusted power is a weighted average of the quality of its space and it is based on the size, duration and quality of its deals.
total_raw_bytes_committed	text	NO	Total provably committed storage power in bytes. Raw byte power is the size of a sector in bytes.
total_raw_bytes_power	text	NO	Total storage power in bytes in the network. Raw byte power is the size of a sector in bytes.

chain_rewards

Reward summaries from the Reward actor.

Name	Type	Nullable	Description
cum_sum_baseline	text	NO	Target that CumsumRealized needs to reach for EffectiveNetworkTime to increase. It is measured in byte-epochs (space * time) representing power committed to the network for some duration.
cum_sum_realized	text	NO	Cumulative sum of network power capped by BaselinePower(epoch). It is measured in byte-epochs (space * time) representing power committed to the network for some duration.
effective_baseline_power	text	NO	The baseline power (in bytes) at the EffectiveNetworkTime epoch.
effective_network_time	bigint	YES	Ceiling of real effective network time "theta" based on CumsumBaselinePower(theta) == CumsumRealizedPower. Theta captures the notion of how much the network has progressed in its baseline and in advancing network time.
height	bigint	NO	Epoch this rewards summary applies to.
new_baseline_power	text	NO	The baseline power (in bytes) the network is targeting.
new_reward	text	YES	The reward to be paid in per WinCount to block producers. The actual reward total paid out depends on the number of winners in any round. This value is recomputed every non-null epoch and used in the next non-null epoch.
new_reward_smoothed_position_estimate	text	NO	Smoothed reward position estimate - Alpha Beta Filter "position" (value) estimate in Q.128 format.
new_reward_smoothed_velocity_estimate	text	NO	Smoothed reward velocity estimate - Alpha Beta Filter "velocity" (rate of change of value) estimate in Q.128 format.
state_root	text	NO	CID of the parent state root.
total_mined_reward	text	NO	The total FIL (attoFIL) awarded to block miners.

QUERY = """
SELECT 
to_timestamp(height_to_unix(cr.height)) as timestamp,
cr.cum_sum_baseline,
cr.cum_sum_realized,
cr.effective_baseline_power,
cr.effective_network_time,
cr.new_baseline_power,
cr.new_reward,
cr.new_reward_smoothed_position_estimate,
cr.new_reward_smoothed_velocity_estimate,
cr.total_mined_reward,
cp.miner_count,
cp.participating_miner_count,
cp.qa_smoothed_position_estimate,
cp.qa_smoothed_velocity_estimate,
cp.state_root,
cp.total_pledge_collateral,
cp.total_qa_bytes_committed,
cp.total_qa_bytes_power,
cp.total_raw_bytes_committed,
cp.total_raw_bytes_power,
ce.burnt_fil,
ce.circulating_fil,
ce.locked_fil,
ce.mined_fil,
ce.vested_fil
FROM chain_rewards cr
LEFT JOIN chain_powers cp
ON cr.state_root = cp.state_root
LEFT JOIN chain_economics ce
ON cr.state_root = ce.parent_state_root
WHERE
to_timestamp(height_to_unix(cr.height)) BETWEEN '2021-06-01' AND '2021-07-01'
"""
chain_economics = (pd.read_sql(QUERY, connection))

chain_economics[['cum_sum_baseline', 'cum_sum_realized',
       'effective_baseline_power', 'effective_network_time',
       'new_baseline_power','new_reward_smoothed_position_estimate',
       'new_reward_smoothed_velocity_estimate', 'total_mined_reward',
       'miner_count', 'participating_miner_count',
       'qa_smoothed_position_estimate','qa_smoothed_velocity_estimate','total_pledge_collateral', 'total_qa_bytes_committed',
       'total_qa_bytes_power', 'total_raw_bytes_committed',
       'total_raw_bytes_power', 'burnt_fil', 'circulating_fil', 'locked_fil',
       'mined_fil', 'vested_fil']] = chain_economics[['cum_sum_baseline', 'cum_sum_realized',
       'effective_baseline_power', 'effective_network_time',
       'new_baseline_power','new_reward_smoothed_position_estimate',
       'new_reward_smoothed_velocity_estimate', 'total_mined_reward',
       'miner_count', 'participating_miner_count',
       'qa_smoothed_position_estimate','qa_smoothed_velocity_estimate', 'total_pledge_collateral', 'total_qa_bytes_committed',
       'total_qa_bytes_power', 'total_raw_bytes_committed',
       'total_raw_bytes_power', 'burnt_fil', 'circulating_fil', 'locked_fil',
       'mined_fil', 'vested_fil']].astype(float)

chain_economics.describe()

	cum_sum_baseline	cum_sum_realized	effective_baseline_power	effective_network_time	new_baseline_power	new_reward	new_reward_smoothed_position_estimate	new_reward_smoothed_velocity_estimate	total_mined_reward	miner_count	...	total_pledge_collateral	total_qa_bytes_committed	total_qa_bytes_power	total_raw_bytes_committed	total_raw_bytes_power	burnt_fil	circulating_fil	locked_fil	mined_fil	vested_fil
count	8.525900e+04	8.525900e+04	8.525900e+04	85259.000000	8.525900e+04	8.525900e+04	8.525900e+04	8.525900e+04	8.525900e+04	85259.000000	...	8.525900e+04	8.525900e+04	8.525900e+04	8.525900e+04	8.525900e+04	8.525900e+04	8.525900e+04	8.525900e+04	8.525900e+04	8.525900e+04
mean	2.117221e+24	2.117219e+24	4.284956e+18	597601.800772	5.059368e+18	1.264016e+20	4.301223e+58	-9.164505e+51	7.589834e+25	541555.566146	...	8.272870e+25	7.396019e+18	7.395577e+18	7.393683e+18	7.393252e+18	2.646491e+25	1.350217e+26	8.273785e+25	7.589834e+25	1.512595e+26
std	1.258826e+23	1.258826e+23	8.300527e+16	29376.941196	8.300524e+16	6.686428e+17	2.275268e+56	1.384736e+50	3.085544e+24	468.881553	...	2.469818e+24	3.621160e+17	3.621347e+17	3.619564e+17	3.619715e+17	2.952578e+23	3.479301e+24	2.470447e+24	3.085544e+24	3.153654e+24
min	1.901761e+24	1.901758e+24	4.142884e+18	546751.000000	4.917297e+18	1.252452e+20	4.261871e+58	-9.407656e+51	7.054874e+25	541144.000000	...	7.830897e+25	6.721132e+18	6.720618e+18	6.719005e+18	6.718506e+18	2.604027e+25	1.290679e+26	7.831719e+25	7.054874e+25	1.458100e+26
25%	2.008047e+24	2.008046e+24	4.212968e+18	572191.500000	4.987381e+18	1.258254e+20	4.281616e+58	-9.283836e+51	7.322973e+25	541366.000000	...	8.061695e+25	7.109558e+18	7.109093e+18	7.107348e+18	7.106899e+18	2.613655e+25	1.320648e+26	8.062548e+25	7.322973e+25	1.485305e+26
50%	2.115896e+24	2.115894e+24	4.284082e+18	597577.000000	5.058495e+18	1.263982e+20	4.301104e+58	-9.162910e+51	7.589920e+25	541488.000000	...	8.279218e+25	7.407435e+18	7.407039e+18	7.405115e+18	7.404737e+18	2.647754e+25	1.349388e+26	8.280132e+25	7.589920e+25	1.512521e+26
75%	2.225168e+24	2.225168e+24	4.356134e+18	622871.500000	5.130548e+18	1.269790e+20	4.320868e+58	-9.044957e+51	7.855009e+25	541575.000000	...	8.486375e+25	7.703864e+18	7.703419e+18	7.701365e+18	7.700921e+18	2.676042e+25	1.379530e+26	8.487347e+25	7.855009e+25	1.539710e+26
max	2.338950e+24	2.338948e+24	4.431161e+18	648769.000000	5.205574e+18	1.275672e+20	4.340886e+58	-8.926758e+51	8.125866e+25	544363.000000	...	8.679158e+25	7.992995e+18	7.992564e+18	7.990300e+18	7.989885e+18	2.685054e+25	1.414348e+26	8.680170e+25	8.125866e+25	1.567617e+26

8 rows × 23 columns

Signal Analysis

chain_economics.fillna(0,inplace=True)

chain_economics['time'] = chain_economics['timestamp'].apply(lambda x: x.value)

time_analysis(chain_economics,'time')

VAR Analysis

timestamps = chain_economics.timestamp.values
del chain_economics['timestamp']
del chain_economics['state_root']
del chain_economics['timestampDiff']
chain_economics.hist(bins=30, figsize=(15, 10))

array([[<AxesSubplot:title={'center':'cum_sum_baseline'}>,
        <AxesSubplot:title={'center':'cum_sum_realized'}>,
        <AxesSubplot:title={'center':'effective_baseline_power'}>,
        <AxesSubplot:title={'center':'effective_network_time'}>,
        <AxesSubplot:title={'center':'new_baseline_power'}>],
       [<AxesSubplot:title={'center':'new_reward'}>,
        <AxesSubplot:title={'center':'new_reward_smoothed_position_estimate'}>,
        <AxesSubplot:title={'center':'new_reward_smoothed_velocity_estimate'}>,
        <AxesSubplot:title={'center':'total_mined_reward'}>,
        <AxesSubplot:title={'center':'miner_count'}>],
       [<AxesSubplot:title={'center':'participating_miner_count'}>,
        <AxesSubplot:title={'center':'qa_smoothed_position_estimate'}>,
        <AxesSubplot:title={'center':'qa_smoothed_velocity_estimate'}>,
        <AxesSubplot:title={'center':'total_pledge_collateral'}>,
        <AxesSubplot:title={'center':'total_qa_bytes_committed'}>],
       [<AxesSubplot:title={'center':'total_qa_bytes_power'}>,
        <AxesSubplot:title={'center':'total_raw_bytes_committed'}>,
        <AxesSubplot:title={'center':'total_raw_bytes_power'}>,
        <AxesSubplot:title={'center':'burnt_fil'}>,
        <AxesSubplot:title={'center':'circulating_fil'}>],
       [<AxesSubplot:title={'center':'locked_fil'}>,
        <AxesSubplot:title={'center':'mined_fil'}>,
        <AxesSubplot:title={'center':'vested_fil'}>,
        <AxesSubplot:title={'center':'time'}>, <AxesSubplot:>]],
      dtype=object)

# normally distribute
log_differenced = pd.DataFrame()
## Difference and log values
for i in chain_economics.columns:
    try:
        log_differenced[i +'_log_differenced'] = np.log(chain_economics[i]).diff()
    except:
        print('Error with:{}'.format(i))

/opt/anaconda3/lib/python3.8/site-packages/pandas/core/arraylike.py:364: RuntimeWarning: invalid value encountered in log
  result = getattr(ufunc, method)(*inputs, **kwargs)

# replace any NA values with zero
log_differenced.fillna(0,inplace=True)

log_differenced.hist(bins=30, figsize=(15, 10))

array([[<AxesSubplot:title={'center':'cum_sum_baseline_log_differenced'}>,
        <AxesSubplot:title={'center':'cum_sum_realized_log_differenced'}>,
        <AxesSubplot:title={'center':'effective_baseline_power_log_differenced'}>,
        <AxesSubplot:title={'center':'effective_network_time_log_differenced'}>,
        <AxesSubplot:title={'center':'new_baseline_power_log_differenced'}>],
       [<AxesSubplot:title={'center':'new_reward_log_differenced'}>,
        <AxesSubplot:title={'center':'new_reward_smoothed_position_estimate_log_differenced'}>,
        <AxesSubplot:title={'center':'new_reward_smoothed_velocity_estimate_log_differenced'}>,
        <AxesSubplot:title={'center':'total_mined_reward_log_differenced'}>,
        <AxesSubplot:title={'center':'miner_count_log_differenced'}>],
       [<AxesSubplot:title={'center':'participating_miner_count_log_differenced'}>,
        <AxesSubplot:title={'center':'qa_smoothed_position_estimate_log_differenced'}>,
        <AxesSubplot:title={'center':'qa_smoothed_velocity_estimate_log_differenced'}>,
        <AxesSubplot:title={'center':'total_pledge_collateral_log_differenced'}>,
        <AxesSubplot:title={'center':'total_qa_bytes_committed_log_differenced'}>],
       [<AxesSubplot:title={'center':'total_qa_bytes_power_log_differenced'}>,
        <AxesSubplot:title={'center':'total_raw_bytes_committed_log_differenced'}>,
        <AxesSubplot:title={'center':'total_raw_bytes_power_log_differenced'}>,
        <AxesSubplot:title={'center':'burnt_fil_log_differenced'}>,
        <AxesSubplot:title={'center':'circulating_fil_log_differenced'}>],
       [<AxesSubplot:title={'center':'locked_fil_log_differenced'}>,
        <AxesSubplot:title={'center':'mined_fil_log_differenced'}>,
        <AxesSubplot:title={'center':'vested_fil_log_differenced'}>,
        <AxesSubplot:title={'center':'time_log_differenced'}>,
        <AxesSubplot:>]], dtype=object)

As a final check prior to modeling, we will run the Augmented Dickey-Fuller test to ensure that our data is stationary (non-unit root - A unit root is a stochastic trend in a time series). The test's hypothesis are:

• $H_O: \textrm{Time series has a unit root}$
• $H_A: \textrm{Time series does not have a unit root}$

for i in log_differenced.columns:
    print(i)
    result = adfuller(log_differenced[i].values)
    print('ADF Statistic: %f' % result[0])
    print('p-value: %f' % result[1])
    if result[1] > 0.05:
        decision = "fail to reject - unit root present"
    else:
        decision = "reject, no unit root present"
    print(decision)
    print('----------------------------------')

cum_sum_baseline_log_differenced
ADF Statistic: -42.616286
p-value: 0.000000
reject, no unit root present
----------------------------------
cum_sum_realized_log_differenced
ADF Statistic: -42.616288
p-value: 0.000000
reject, no unit root present
----------------------------------
effective_baseline_power_log_differenced
ADF Statistic: -42.756111
p-value: 0.000000
reject, no unit root present
----------------------------------
effective_network_time_log_differenced
ADF Statistic: -42.584411
p-value: 0.000000
reject, no unit root present
----------------------------------
new_baseline_power_log_differenced
ADF Statistic: -42.766353
p-value: 0.000000
reject, no unit root present
----------------------------------
new_reward_log_differenced
ADF Statistic: -42.732455
p-value: 0.000000
reject, no unit root present
----------------------------------
new_reward_smoothed_position_estimate_log_differenced
ADF Statistic: -42.732460
p-value: 0.000000
reject, no unit root present
----------------------------------
new_reward_smoothed_velocity_estimate_log_differenced

/opt/anaconda3/lib/python3.8/site-packages/statsmodels/regression/linear_model.py:903: RuntimeWarning: divide by zero encountered in log
  llf = -nobs2*np.log(2*np.pi) - nobs2*np.log(ssr / nobs) - nobs2

ADF Statistic: nan
p-value: nan
reject, no unit root present
----------------------------------
total_mined_reward_log_differenced
ADF Statistic: -42.598322
p-value: 0.000000
reject, no unit root present
----------------------------------
miner_count_log_differenced
ADF Statistic: -43.960423
p-value: 0.000000
reject, no unit root present
----------------------------------
participating_miner_count_log_differenced
ADF Statistic: -41.754532
p-value: 0.000000
reject, no unit root present
----------------------------------
qa_smoothed_position_estimate_log_differenced
ADF Statistic: -41.972755
p-value: 0.000000
reject, no unit root present
----------------------------------
qa_smoothed_velocity_estimate_log_differenced
ADF Statistic: -29.128841
p-value: 0.000000
reject, no unit root present
----------------------------------
total_pledge_collateral_log_differenced
ADF Statistic: -42.422216
p-value: 0.000000
reject, no unit root present
----------------------------------
total_qa_bytes_committed_log_differenced
ADF Statistic: -41.957639
p-value: 0.000000
reject, no unit root present
----------------------------------
total_qa_bytes_power_log_differenced
ADF Statistic: -41.957249
p-value: 0.000000
reject, no unit root present
----------------------------------
total_raw_bytes_committed_log_differenced
ADF Statistic: -41.957256
p-value: 0.000000
reject, no unit root present
----------------------------------
total_raw_bytes_power_log_differenced
ADF Statistic: -41.956858
p-value: 0.000000
reject, no unit root present
----------------------------------
burnt_fil_log_differenced
ADF Statistic: -41.641283
p-value: 0.000000
reject, no unit root present
----------------------------------
circulating_fil_log_differenced
ADF Statistic: -42.880082
p-value: 0.000000
reject, no unit root present
----------------------------------
locked_fil_log_differenced
ADF Statistic: -42.422274
p-value: 0.000000
reject, no unit root present
----------------------------------
mined_fil_log_differenced
ADF Statistic: -42.598322
p-value: 0.000000
reject, no unit root present
----------------------------------
vested_fil_log_differenced
ADF Statistic: -42.694020
p-value: 0.000000
reject, no unit root present
----------------------------------
time_log_differenced
ADF Statistic: -42.764751
p-value: 0.000000
reject, no unit root present
----------------------------------

# removed several columns because of VAR errors
log_differenced_subset = log_differenced[['cum_sum_baseline_log_differenced', 'cum_sum_realized_log_differenced',
                                       'effective_baseline_power_log_differenced','effective_network_time_log_differenced',
                                       'new_baseline_power_log_differenced','total_mined_reward_log_differenced',
                                       'miner_count_log_differenced','participating_miner_count_log_differenced',
                                       'qa_smoothed_position_estimate_log_differenced','qa_smoothed_velocity_estimate_log_differenced',
                                       'total_pledge_collateral_log_differenced','total_qa_bytes_committed_log_differenced',
                                       'total_qa_bytes_power_log_differenced','total_raw_bytes_committed_log_differenced',
                                       'total_raw_bytes_power_log_differenced','burnt_fil_log_differenced','circulating_fil_log_differenced',
                                       'locked_fil_log_differenced','vested_fil_log_differenced']]

# var model
aic = []
for i in range(1,16):
    model = VAR(log_differenced_subset)
    results = model.fit(i)
    aic.append(results.aic)

plt.figure(figsize=(10, 8))
plt.plot(aic, 'r+')
plt.legend(['AIC'])
plt.xlabel('Autocorrelation Lag')
plt.ylabel('AIC')
plt.title('Plot of sweeps over lag depths over AIC Loss function')
plt.show()

# instantiate the var model object from statsmodels
model = VAR(log_differenced_subset)

# fit model with determined lag values
results = model.fit(4)

results.summary()

  Summary of Regression Results   
==================================
Model:                         VAR
Method:                        OLS
Date:           Mon, 09, Aug, 2021
Time:                     14:43:23
--------------------------------------------------------------------
No. of Equations:         19.0000    BIC:                   -481.427
Nobs:                     85255.0    HQIC:                  -481.538
Log likelihood:       1.82319e+07    FPE:               7.06629e-210
AIC:                     -481.588    Det(Omega_mle):    6.94285e-210
--------------------------------------------------------------------
Results for equation cum_sum_baseline_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000017            0.009           0.993
L1.cum_sum_baseline_log_differenced                  14599.097968      4839.103413            3.017           0.003
L1.cum_sum_realized_log_differenced                   -123.598688       588.423076           -0.210           0.834
L1.effective_baseline_power_log_differenced          -8285.051948      2406.932943           -3.442           0.001
L1.effective_network_time_log_differenced           -14333.636188      5107.361547           -2.806           0.005
L1.new_baseline_power_log_differenced                  119.627556      2136.697713            0.056           0.955
L1.total_mined_reward_log_differenced                  121.101608        53.555185            2.261           0.024
L1.miner_count_log_differenced                           0.876370         0.461036            1.901           0.057
L1.participating_miner_count_log_differenced             0.930315         0.113096            8.226           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.640999         0.267535            2.396           0.017
L1.qa_smoothed_velocity_estimate_log_differenced        -0.004605         0.001568           -2.937           0.003
L1.total_pledge_collateral_log_differenced           -9351.582277      1547.196992           -6.044           0.000
L1.total_qa_bytes_committed_log_differenced          -4314.853324       749.409735           -5.758           0.000
L1.total_qa_bytes_power_log_differenced               3605.840936       743.479677            4.850           0.000
L1.total_raw_bytes_committed_log_differenced          4654.694709       750.757738            6.200           0.000
L1.total_raw_bytes_power_log_differenced             -3945.521406       744.706335           -5.298           0.000
L1.burnt_fil_log_differenced                           -33.931504        19.562884           -1.734           0.083
L1.circulating_fil_log_differenced                    -167.878640        99.572478           -1.686           0.092
L1.locked_fil_log_differenced                         9252.364886      1527.802464            6.056           0.000
L1.vested_fil_log_differenced                          229.708705       245.645923            0.935           0.350
L2.cum_sum_baseline_log_differenced                  34226.982592      5107.084992            6.702           0.000
L2.cum_sum_realized_log_differenced                     72.798849       631.626773            0.115           0.908
L2.effective_baseline_power_log_differenced         -19064.653319      2526.175573           -7.547           0.000
L2.effective_network_time_log_differenced           -33895.468189      5402.357139           -6.274           0.000
L2.new_baseline_power_log_differenced                 -367.726755      2303.349059           -0.160           0.873
L2.total_mined_reward_log_differenced                  -36.486894        53.496523           -0.682           0.495
L2.miner_count_log_differenced                           0.230174         0.461428            0.499           0.618
L2.participating_miner_count_log_differenced             0.398151         0.113089            3.521           0.000
L2.qa_smoothed_position_estimate_log_differenced         1.200750         0.267062            4.496           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.001365         0.001599            0.854           0.393
L2.total_pledge_collateral_log_differenced           -7251.986652      1551.410061           -4.674           0.000
L2.total_qa_bytes_committed_log_differenced          -3463.036188       750.661462           -4.613           0.000
L2.total_qa_bytes_power_log_differenced               2839.643858       744.406268            3.815           0.000
L2.total_raw_bytes_committed_log_differenced          3334.555543       751.702089            4.436           0.000
L2.total_raw_bytes_power_log_differenced             -2712.185030       745.334905           -3.639           0.000
L2.burnt_fil_log_differenced                            28.386030        19.546396            1.452           0.146
L2.circulating_fil_log_differenced                     122.616224        99.484551            1.233           0.218
L2.locked_fil_log_differenced                         7332.953915      1532.062911            4.786           0.000
L2.vested_fil_log_differenced                         -143.829167       289.487250           -0.497           0.619
L3.cum_sum_baseline_log_differenced                   3131.522359      5102.495723            0.614           0.539
L3.cum_sum_realized_log_differenced                     13.760471       631.446520            0.022           0.983
L3.effective_baseline_power_log_differenced          -1705.910101      2527.783705           -0.675           0.500
L3.effective_network_time_log_differenced            -3085.106865      5396.579369           -0.572           0.568
L3.new_baseline_power_log_differenced                   58.070452      2302.427361            0.025           0.980
L3.total_mined_reward_log_differenced                  105.499706        53.457272            1.974           0.048
L3.miner_count_log_differenced                           0.624708         0.461671            1.353           0.176
L3.participating_miner_count_log_differenced            -0.097219         0.113100           -0.860           0.390
L3.qa_smoothed_position_estimate_log_differenced        -0.422182         0.267066           -1.581           0.114
L3.qa_smoothed_velocity_estimate_log_differenced         0.003498         0.001599            2.188           0.029
L3.total_pledge_collateral_log_differenced             273.899747      1551.316327            0.177           0.860
L3.total_qa_bytes_committed_log_differenced           -203.071863       750.228669           -0.271           0.787
L3.total_qa_bytes_power_log_differenced                 56.794830       744.002187            0.076           0.939
L3.total_raw_bytes_committed_log_differenced          -180.692848       751.215298           -0.241           0.810
L3.total_raw_bytes_power_log_differenced               327.581860       744.876326            0.440           0.660
L3.burnt_fil_log_differenced                           -48.681078        19.534968           -2.492           0.013
L3.circulating_fil_log_differenced                    -250.965646        99.426031           -2.524           0.012
L3.locked_fil_log_differenced                         -421.973383      1531.959515           -0.275           0.783
L3.vested_fil_log_differenced                          181.855653       289.275637            0.629           0.530
L4.cum_sum_baseline_log_differenced                   5545.585682      4826.249611            1.149           0.251
L4.cum_sum_realized_log_differenced                     93.362686       588.367403            0.159           0.874
L4.effective_baseline_power_log_differenced          -2602.798549      2405.273392           -1.082           0.279
L4.effective_network_time_log_differenced            -5647.126730      5093.262655           -1.109           0.268
L4.new_baseline_power_log_differenced                 -536.325802      2135.974758           -0.251           0.802
L4.total_mined_reward_log_differenced                  346.598805        53.493301            6.479           0.000
L4.miner_count_log_differenced                           1.760502         0.461637            3.814           0.000
L4.participating_miner_count_log_differenced             0.348774         0.113032            3.086           0.002
L4.qa_smoothed_position_estimate_log_differenced        -1.290534         0.266758           -4.838           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.001023         0.001565            0.654           0.513
L4.total_pledge_collateral_log_differenced           -4763.168125      1549.931696           -3.073           0.002
L4.total_qa_bytes_committed_log_differenced            565.638427       748.384788            0.756           0.450
L4.total_qa_bytes_power_log_differenced              -1117.379038       742.347155           -1.505           0.132
L4.total_raw_bytes_committed_log_differenced          -367.187415       749.455270           -0.490           0.624
L4.total_raw_bytes_power_log_differenced               918.202465       743.303132            1.235           0.217
L4.burnt_fil_log_differenced                          -120.139694        19.557992           -6.143           0.000
L4.circulating_fil_log_differenced                    -620.856480        99.535641           -6.238           0.000
L4.locked_fil_log_differenced                         4397.979460      1530.515890            2.874           0.004
L4.vested_fil_log_differenced                          748.795137       244.516792            3.062           0.002
===================================================================================================================

Results for equation cum_sum_realized_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000017            0.009           0.993
L1.cum_sum_baseline_log_differenced                  14600.152315      4839.106315            3.017           0.003
L1.cum_sum_realized_log_differenced                   -124.242445       588.423428           -0.211           0.833
L1.effective_baseline_power_log_differenced          -8285.112424      2406.934387           -3.442           0.001
L1.effective_network_time_log_differenced           -14334.042446      5107.364611           -2.807           0.005
L1.new_baseline_power_log_differenced                  119.457368      2136.698995            0.056           0.955
L1.total_mined_reward_log_differenced                  121.107742        53.555217            2.261           0.024
L1.miner_count_log_differenced                           0.876420         0.461037            1.901           0.057
L1.participating_miner_count_log_differenced             0.930315         0.113096            8.226           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.640969         0.267535            2.396           0.017
L1.qa_smoothed_velocity_estimate_log_differenced        -0.004605         0.001568           -2.937           0.003
L1.total_pledge_collateral_log_differenced           -9351.489385      1547.197920           -6.044           0.000
L1.total_qa_bytes_committed_log_differenced          -4314.809969       749.410184           -5.758           0.000
L1.total_qa_bytes_power_log_differenced               3605.804405       743.480123            4.850           0.000
L1.total_raw_bytes_committed_log_differenced          4654.650064       750.758188            6.200           0.000
L1.total_raw_bytes_power_log_differenced             -3945.483575       744.706782           -5.298           0.000
L1.burnt_fil_log_differenced                           -33.933340        19.562895           -1.735           0.083
L1.circulating_fil_log_differenced                    -167.888765        99.572537           -1.686           0.092
L1.locked_fil_log_differenced                         9252.265977      1527.803380            6.056           0.000
L1.vested_fil_log_differenced                          229.695541       245.646070            0.935           0.350
L2.cum_sum_baseline_log_differenced                  34223.075124      5107.088055            6.701           0.000
L2.cum_sum_realized_log_differenced                     71.092829       631.627152            0.113           0.910
L2.effective_baseline_power_log_differenced         -19064.876233      2526.177088           -7.547           0.000
L2.effective_network_time_log_differenced           -33889.850002      5402.360380           -6.273           0.000
L2.new_baseline_power_log_differenced                 -363.947513      2303.350441           -0.158           0.874
L2.total_mined_reward_log_differenced                  -36.495658        53.496555           -0.682           0.495
L2.miner_count_log_differenced                           0.230187         0.461429            0.499           0.618
L2.participating_miner_count_log_differenced             0.398137         0.113089            3.521           0.000
L2.qa_smoothed_position_estimate_log_differenced         1.200779         0.267062            4.496           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.001365         0.001599            0.854           0.393
L2.total_pledge_collateral_log_differenced           -7251.745681      1551.410992           -4.674           0.000
L2.total_qa_bytes_committed_log_differenced          -3463.003617       750.661913           -4.613           0.000
L2.total_qa_bytes_power_log_differenced               2839.608888       744.406714            3.815           0.000
L2.total_raw_bytes_committed_log_differenced          3334.537404       751.702540            4.436           0.000
L2.total_raw_bytes_power_log_differenced             -2712.164509       745.335352           -3.639           0.000
L2.burnt_fil_log_differenced                            28.389370        19.546408            1.452           0.146
L2.circulating_fil_log_differenced                     122.633425        99.484611            1.233           0.218
L2.locked_fil_log_differenced                         7332.723451      1532.063830            4.786           0.000
L2.vested_fil_log_differenced                         -143.849224       289.487423           -0.497           0.619
L3.cum_sum_baseline_log_differenced                   3126.114691      5102.498783            0.613           0.540
L3.cum_sum_realized_log_differenced                     11.597284       631.446899            0.018           0.985
L3.effective_baseline_power_log_differenced          -1706.549243      2527.785221           -0.675           0.500
L3.effective_network_time_log_differenced            -3077.528779      5396.582606           -0.570           0.568
L3.new_baseline_power_log_differenced                   63.526648      2302.428742            0.028           0.978
L3.total_mined_reward_log_differenced                  105.505659        53.457304            1.974           0.048
L3.miner_count_log_differenced                           0.624688         0.461671            1.353           0.176
L3.participating_miner_count_log_differenced            -0.097201         0.113100           -0.859           0.390
L3.qa_smoothed_position_estimate_log_differenced        -0.422100         0.267066           -1.581           0.114
L3.qa_smoothed_velocity_estimate_log_differenced         0.003498         0.001599            2.188           0.029
L3.total_pledge_collateral_log_differenced             273.724451      1551.317257            0.176           0.860
L3.total_qa_bytes_committed_log_differenced           -203.040278       750.229119           -0.271           0.787
L3.total_qa_bytes_power_log_differenced                 56.761025       744.002633            0.076           0.939
L3.total_raw_bytes_committed_log_differenced          -180.722046       751.215749           -0.241           0.810
L3.total_raw_bytes_power_log_differenced               327.613215       744.876773            0.440           0.660
L3.burnt_fil_log_differenced                           -48.683649        19.534980           -2.492           0.013
L3.circulating_fil_log_differenced                    -250.978252        99.426091           -2.524           0.012
L3.locked_fil_log_differenced                         -421.805611      1531.960434           -0.275           0.783
L3.vested_fil_log_differenced                          181.902592       289.275811            0.629           0.529
L4.cum_sum_baseline_log_differenced                   5535.662187      4826.252506            1.147           0.251
L4.cum_sum_realized_log_differenced                     90.104678       588.367756            0.153           0.878
L4.effective_baseline_power_log_differenced          -2604.014091      2405.274835           -1.083           0.279
L4.effective_network_time_log_differenced            -5633.927870      5093.265710           -1.106           0.269
L4.new_baseline_power_log_differenced                 -526.707339      2135.976039           -0.247           0.805
L4.total_mined_reward_log_differenced                  346.597559        53.493333            6.479           0.000
L4.miner_count_log_differenced                           1.760556         0.461638            3.814           0.000
L4.participating_miner_count_log_differenced             0.348772         0.113032            3.086           0.002
L4.qa_smoothed_position_estimate_log_differenced        -1.290527         0.266758           -4.838           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.001023         0.001565            0.654           0.513
L4.total_pledge_collateral_log_differenced           -4762.940395      1549.932625           -3.073           0.002
L4.total_qa_bytes_committed_log_differenced            565.768946       748.385237            0.756           0.450
L4.total_qa_bytes_power_log_differenced              -1117.513483       742.347600           -1.505           0.132
L4.total_raw_bytes_committed_log_differenced          -367.321857       749.455720           -0.490           0.624
L4.total_raw_bytes_power_log_differenced               918.340855       743.303578            1.235           0.217
L4.burnt_fil_log_differenced                          -120.138848        19.558003           -6.143           0.000
L4.circulating_fil_log_differenced                    -620.852295        99.535701           -6.237           0.000
L4.locked_fil_log_differenced                         4397.754154      1530.516808            2.873           0.004
L4.vested_fil_log_differenced                          748.833085       244.516939            3.062           0.002
===================================================================================================================

Results for equation effective_baseline_power_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000006            0.009           0.992
L1.cum_sum_baseline_log_differenced                   4901.353921      1596.339945            3.070           0.002
L1.cum_sum_realized_log_differenced                    -37.216881       194.111012           -0.192           0.848
L1.effective_baseline_power_log_differenced          -2771.372868       794.007252           -3.490           0.000
L1.effective_network_time_log_differenced            -4816.639907      1684.833854           -2.859           0.004
L1.new_baseline_power_log_differenced                   24.263612       704.861132            0.034           0.973
L1.total_mined_reward_log_differenced                   38.977228        17.666967            2.206           0.027
L1.miner_count_log_differenced                           0.286870         0.152088            1.886           0.059
L1.participating_miner_count_log_differenced             0.310308         0.037308            8.317           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.206629         0.088255            2.341           0.019
L1.qa_smoothed_velocity_estimate_log_differenced        -0.001491         0.000517           -2.883           0.004
L1.total_pledge_collateral_log_differenced           -3060.980411       510.394623           -5.997           0.000
L1.total_qa_bytes_committed_log_differenced          -1439.548372       247.217840           -5.823           0.000
L1.total_qa_bytes_power_log_differenced               1209.915197       245.261613            4.933           0.000
L1.total_raw_bytes_committed_log_differenced          1552.304079       247.662524            6.268           0.000
L1.total_raw_bytes_power_log_differenced             -1322.613968       245.666267           -5.384           0.000
L1.burnt_fil_log_differenced                           -10.885852         6.453471           -1.687           0.092
L1.circulating_fil_log_differenced                     -53.794724        32.847309           -1.638           0.101
L1.locked_fil_log_differenced                         3029.253507       503.996690            6.010           0.000
L1.vested_fil_log_differenced                           75.976327        81.034515            0.938           0.348
L2.cum_sum_baseline_log_differenced                  11443.516129      1684.742623            6.792           0.000
L2.cum_sum_realized_log_differenced                     26.110661       208.363195            0.125           0.900
L2.effective_baseline_power_log_differenced          -6369.632299       833.343417           -7.643           0.000
L2.effective_network_time_log_differenced           -11334.446856      1782.148006           -6.360           0.000
L2.new_baseline_power_log_differenced                 -128.961978       759.836647           -0.170           0.865
L2.total_mined_reward_log_differenced                  -12.035183        17.647615           -0.682           0.495
L2.miner_count_log_differenced                           0.069208         0.152218            0.455           0.649
L2.participating_miner_count_log_differenced             0.132286         0.037306            3.546           0.000
L2.qa_smoothed_position_estimate_log_differenced         0.399451         0.088099            4.534           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.000452         0.000527            0.858           0.391
L2.total_pledge_collateral_log_differenced           -2372.730280       511.784445           -4.636           0.000
L2.total_qa_bytes_committed_log_differenced          -1146.637454       247.630764           -4.630           0.000
L2.total_qa_bytes_power_log_differenced                943.989989       245.567280            3.844           0.000
L2.total_raw_bytes_committed_log_differenced          1103.580849       247.974050            4.450           0.000
L2.total_raw_bytes_power_log_differenced              -901.275751       245.873622           -3.666           0.000
L2.burnt_fil_log_differenced                             9.386025         6.448032            1.456           0.145
L2.circulating_fil_log_differenced                      40.401751        32.818303            1.231           0.218
L2.locked_fil_log_differenced                         2399.448592       505.402141            4.748           0.000
L2.vested_fil_log_differenced                          -47.405596        95.497042           -0.496           0.620
L3.cum_sum_baseline_log_differenced                   1073.106235      1683.228699            0.638           0.524
L3.cum_sum_realized_log_differenced                      2.076959       208.303733            0.010           0.992
L3.effective_baseline_power_log_differenced           -592.889085       833.873914           -0.711           0.477
L3.effective_network_time_log_differenced            -1054.540304      1780.242016           -0.592           0.554
L3.new_baseline_power_log_differenced                   28.905204       759.532594            0.038           0.970
L3.total_mined_reward_log_differenced                   34.465435        17.634667            1.954           0.051
L3.miner_count_log_differenced                           0.205637         0.152297            1.350           0.177
L3.participating_miner_count_log_differenced            -0.034042         0.037310           -0.912           0.362
L3.qa_smoothed_position_estimate_log_differenced        -0.145107         0.088101           -1.647           0.100
L3.qa_smoothed_velocity_estimate_log_differenced         0.001151         0.000527            2.183           0.029
L3.total_pledge_collateral_log_differenced             117.233149       511.753523            0.229           0.819
L3.total_qa_bytes_committed_log_differenced            -88.996041       247.487993           -0.360           0.719
L3.total_qa_bytes_power_log_differenced                 42.472753       245.433980            0.173           0.863
L3.total_raw_bytes_committed_log_differenced           -38.319559       247.813466           -0.155           0.877
L3.total_raw_bytes_power_log_differenced                85.050795       245.722344            0.346           0.729
L3.burnt_fil_log_differenced                           -15.992484         6.444262           -2.482           0.013
L3.circulating_fil_log_differenced                     -82.497833        32.798998           -2.515           0.012
L3.locked_fil_log_differenced                         -165.878518       505.368032           -0.328           0.743
L3.vested_fil_log_differenced                           59.815748        95.427234            0.627           0.531
L4.cum_sum_baseline_log_differenced                   1893.481459      1592.099689            1.189           0.234
L4.cum_sum_realized_log_differenced                     27.127456       194.092646            0.140           0.889
L4.effective_baseline_power_log_differenced           -904.268738       793.459794           -1.140           0.254
L4.effective_network_time_log_differenced            -1922.486858      1680.182863           -1.144           0.253
L4.new_baseline_power_log_differenced                 -165.682156       704.622641           -0.235           0.814
L4.total_mined_reward_log_differenced                  113.894863        17.646553            6.454           0.000
L4.miner_count_log_differenced                           0.580770         0.152287            3.814           0.000
L4.participating_miner_count_log_differenced             0.115878         0.037287            3.108           0.002
L4.qa_smoothed_position_estimate_log_differenced        -0.425983         0.087999           -4.841           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000335         0.000516            0.650           0.516
L4.total_pledge_collateral_log_differenced           -1549.470430       511.296756           -3.030           0.002
L4.total_qa_bytes_committed_log_differenced            181.710631       246.879727            0.736           0.462
L4.total_qa_bytes_power_log_differenced               -361.930170       244.888012           -1.478           0.139
L4.total_raw_bytes_committed_log_differenced          -117.209407       247.232862           -0.474           0.635
L4.total_raw_bytes_power_log_differenced               297.191942       245.203373            1.212           0.226
L4.burnt_fil_log_differenced                           -39.520856         6.451857           -6.126           0.000
L4.circulating_fil_log_differenced                    -204.314347        32.835157           -6.222           0.000
L4.locked_fil_log_differenced                         1429.332141       504.891804            2.831           0.005
L4.vested_fil_log_differenced                          248.455766        80.662034            3.080           0.002
===================================================================================================================

Results for equation effective_network_time_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000014            0.009           0.993
L1.cum_sum_baseline_log_differenced                  11981.602428      3987.852617            3.005           0.003
L1.cum_sum_realized_log_differenced                   -103.896563       484.913072           -0.214           0.830
L1.effective_baseline_power_log_differenced          -6805.454111      1983.527323           -3.431           0.001
L1.effective_network_time_log_differenced           -11761.202425      4208.921235           -2.794           0.005
L1.new_baseline_power_log_differenced                  107.312949      1760.829402            0.061           0.951
L1.total_mined_reward_log_differenced                  100.352554        44.134247            2.274           0.023
L1.miner_count_log_differenced                           0.723458         0.379935            1.904           0.057
L1.participating_miner_count_log_differenced             0.764682         0.093201            8.205           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.531006         0.220473            2.408           0.016
L1.qa_smoothed_velocity_estimate_log_differenced        -0.003811         0.001292           -2.949           0.003
L1.total_pledge_collateral_log_differenced           -7719.970861      1275.028253           -6.055           0.000
L1.total_qa_bytes_committed_log_differenced          -3546.433935       617.580431           -5.742           0.000
L1.total_qa_bytes_power_log_differenced               2959.726664       612.693535            4.831           0.000
L1.total_raw_bytes_committed_log_differenced          3826.115828       618.691306            6.184           0.000
L1.total_raw_bytes_power_log_differenced             -3239.278179       613.704410           -5.278           0.000
L1.burnt_fil_log_differenced                           -28.138007        16.121560           -1.745           0.081
L1.circulating_fil_log_differenced                    -139.251472        82.056598           -1.697           0.090
L1.locked_fil_log_differenced                         7637.634421      1259.045433            6.066           0.000
L1.vested_fil_log_differenced                          189.179406       202.434140            0.935           0.350
L2.cum_sum_baseline_log_differenced                  28117.847392      4208.693328            6.681           0.000
L2.cum_sum_realized_log_differenced                     58.786787       520.516770            0.113           0.910
L2.effective_baseline_power_log_differenced         -15664.402281      2081.793880           -7.524           0.000
L2.effective_network_time_log_differenced           -27844.486866      4452.023902           -6.254           0.000
L2.new_baseline_power_log_differenced                 -298.632595      1898.164968           -0.157           0.875
L2.total_mined_reward_log_differenced                  -30.067751        44.085904           -0.682           0.495
L2.miner_count_log_differenced                           0.193529         0.380258            0.509           0.611
L2.participating_miner_count_log_differenced             0.327562         0.093195            3.515           0.000
L2.qa_smoothed_position_estimate_log_differenced         0.987580         0.220083            4.487           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.001124         0.001317            0.853           0.394
L2.total_pledge_collateral_log_differenced           -5987.325557      1278.500198           -4.683           0.000
L2.total_qa_bytes_committed_log_differenced          -2851.340547       618.611966           -4.609           0.000
L2.total_qa_bytes_power_log_differenced               2335.908591       613.457128            3.808           0.000
L2.total_raw_bytes_committed_log_differenced          2745.850372       619.469535            4.433           0.000
L2.total_raw_bytes_power_log_differenced             -2231.257429       614.222408           -3.633           0.000
L2.burnt_fil_log_differenced                            23.379085        16.107973            1.451           0.147
L2.circulating_fil_log_differenced                     101.069465        81.984139            1.233           0.218
L2.locked_fil_log_differenced                         6054.042124      1262.556422            4.795           0.000
L2.vested_fil_log_differenced                         -118.545259       238.563302           -0.497           0.619
L3.cum_sum_baseline_log_differenced                   2557.659660      4204.911362            0.608           0.543
L3.cum_sum_realized_log_differenced                     12.749264       520.368226            0.025           0.980
L3.effective_baseline_power_log_differenced          -1388.537645      2083.119124           -0.667           0.505
L3.effective_network_time_log_differenced            -2521.273415      4447.262504           -0.567           0.571
L3.new_baseline_power_log_differenced                   42.270750      1897.405406            0.022           0.982
L3.total_mined_reward_log_differenced                   87.132535        44.053558            1.978           0.048
L3.miner_count_log_differenced                           0.515052         0.380458            1.354           0.176
L3.participating_miner_count_log_differenced            -0.078982         0.093205           -0.847           0.397
L3.qa_smoothed_position_estimate_log_differenced        -0.344552         0.220086           -1.566           0.117
L3.qa_smoothed_velocity_estimate_log_differenced         0.002884         0.001317            2.189           0.029
L3.total_pledge_collateral_log_differenced             210.291088      1278.422953            0.164           0.869
L3.total_qa_bytes_committed_log_differenced           -154.714384       618.255306           -0.250           0.802
L3.total_qa_bytes_power_log_differenced                 33.181244       613.124130            0.054           0.957
L3.total_raw_bytes_committed_log_differenced          -161.121253       619.068376           -0.260           0.795
L3.total_raw_bytes_power_log_differenced               283.155216       613.844498            0.461           0.645
L3.burnt_fil_log_differenced                           -40.154799        16.098555           -2.494           0.013
L3.circulating_fil_log_differenced                    -206.980436        81.935913           -2.526           0.012
L3.locked_fil_log_differenced                         -332.429759      1262.471214           -0.263           0.792
L3.vested_fil_log_differenced                          149.963980       238.388914            0.629           0.529
L4.cum_sum_baseline_log_differenced                   4533.180713      3977.259938            1.140           0.254
L4.cum_sum_realized_log_differenced                     79.033492       484.867193            0.163           0.871
L4.effective_baseline_power_log_differenced          -2118.725433      1982.159705           -1.069           0.285
L4.effective_network_time_log_differenced            -4619.423521      4197.302491           -1.101           0.271
L4.new_baseline_power_log_differenced                 -448.383124      1760.233622           -0.255           0.799
L4.total_mined_reward_log_differenced                  285.874995        44.083249            6.485           0.000
L4.miner_count_log_differenced                           1.450752         0.380430            3.813           0.000
L4.participating_miner_count_log_differenced             0.286941         0.093148            3.080           0.002
L4.qa_smoothed_position_estimate_log_differenced        -1.063334         0.219833           -4.837           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000845         0.001289            0.655           0.512
L4.total_pledge_collateral_log_differenced           -3937.668778      1277.281893           -3.083           0.002
L4.total_qa_bytes_committed_log_differenced            468.931008       616.735784            0.760           0.447
L4.total_qa_bytes_power_log_differenced               -924.625793       611.760236           -1.511           0.131
L4.total_raw_bytes_committed_log_differenced          -304.840744       617.617957           -0.494           0.622
L4.total_raw_bytes_power_log_differenced               759.936266       612.548046            1.241           0.215
L4.burnt_fil_log_differenced                           -99.067265        16.117529           -6.147           0.000
L4.circulating_fil_log_differenced                    -511.913334        82.026242           -6.241           0.000
L4.locked_fil_log_differenced                         3636.537808      1261.281539            2.883           0.004
L4.vested_fil_log_differenced                          616.234066       201.503635            3.058           0.002
===================================================================================================================

Results for equation new_baseline_power_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000005            0.010           0.992
L1.cum_sum_baseline_log_differenced                   4161.852480      1353.393966            3.075           0.002
L1.cum_sum_realized_log_differenced                    -31.298826       164.569378           -0.190           0.849
L1.effective_baseline_power_log_differenced          -2351.900157       673.167784           -3.494           0.000
L1.effective_network_time_log_differenced            -4090.242633      1428.420042           -2.863           0.004
L1.new_baseline_power_log_differenced                   18.812885       597.588757            0.031           0.975
L1.total_mined_reward_log_differenced                   32.985818        14.978242            2.202           0.028
L1.miner_count_log_differenced                           0.243091         0.128942            1.885           0.059
L1.participating_miner_count_log_differenced             0.263293         0.031631            8.324           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.174849         0.074824            2.337           0.019
L1.qa_smoothed_velocity_estimate_log_differenced        -0.001262         0.000438           -2.879           0.004
L1.total_pledge_collateral_log_differenced           -2593.650604       432.717984           -5.994           0.000
L1.total_qa_bytes_committed_log_differenced          -1221.473938       209.593912           -5.828           0.000
L1.total_qa_bytes_power_log_differenced               1027.052214       207.935401            4.939           0.000
L1.total_raw_bytes_committed_log_differenced          1317.105248       209.970919            6.273           0.000
L1.total_raw_bytes_power_log_differenced             -1122.634987       208.278471           -5.390           0.000
L1.burnt_fil_log_differenced                            -9.210269         5.471321           -1.683           0.092
L1.circulating_fil_log_differenced                     -45.510654        27.848297           -1.634           0.102
L1.locked_fil_log_differenced                         2566.813684       427.293748            6.007           0.000
L1.vested_fil_log_differenced                           64.422792        68.701923            0.938           0.348
L2.cum_sum_baseline_log_differenced                   9710.828600      1428.342696            6.799           0.000
L2.cum_sum_realized_log_differenced                     21.987756       176.652531            0.124           0.901
L2.effective_baseline_power_log_differenced          -5405.070939       706.517403           -7.650           0.000
L2.effective_network_time_log_differenced            -9618.100789      1510.924015           -6.366           0.000
L2.new_baseline_power_log_differenced                 -109.458889       644.197582           -0.170           0.865
L2.total_mined_reward_log_differenced                  -10.206661        14.961836           -0.682           0.495
L2.miner_count_log_differenced                           0.058262         0.129052            0.451           0.652
L2.participating_miner_count_log_differenced             0.112206         0.031628            3.548           0.000
L2.qa_smoothed_position_estimate_log_differenced         0.338868         0.074691            4.537           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.000384         0.000447            0.858           0.391
L2.total_pledge_collateral_log_differenced           -2010.302538       433.896290           -4.633           0.000
L2.total_qa_bytes_committed_log_differenced           -972.360519       209.943993           -4.632           0.000
L2.total_qa_bytes_power_log_differenced                800.739573       208.194549            3.846           0.000
L2.total_raw_bytes_committed_log_differenced           935.818879       210.235034            4.451           0.000
L2.total_raw_bytes_power_log_differenced              -764.488522       208.454269           -3.667           0.000
L2.burnt_fil_log_differenced                             7.960158         5.466710            1.456           0.145
L2.circulating_fil_log_differenced                      34.256487        27.823706            1.231           0.218
L2.locked_fil_log_differenced                         2032.958973       428.485305            4.745           0.000
L2.vested_fil_log_differenced                          -40.197472        80.963407           -0.496           0.620
L3.cum_sum_baseline_log_differenced                    911.418833      1427.059175            0.639           0.523
L3.cum_sum_realized_log_differenced                      1.191227       176.602118            0.007           0.995
L3.effective_baseline_power_log_differenced           -504.581902       706.967164           -0.714           0.475
L3.effective_network_time_log_differenced             -895.060055      1509.308096           -0.593           0.553
L3.new_baseline_power_log_differenced                   25.967833       643.939803            0.040           0.968
L3.total_mined_reward_log_differenced                   29.199179        14.950858            1.953           0.051
L3.miner_count_log_differenced                           0.174307         0.129119            1.350           0.177
L3.participating_miner_count_log_differenced            -0.028982         0.031632           -0.916           0.360
L3.qa_smoothed_position_estimate_log_differenced        -0.123372         0.074693           -1.652           0.099
L3.qa_smoothed_velocity_estimate_log_differenced         0.000976         0.000447            2.182           0.029
L3.total_pledge_collateral_log_differenced             101.033412       433.870074            0.233           0.816
L3.total_qa_bytes_committed_log_differenced            -76.835612       209.822950           -0.366           0.714
L3.total_qa_bytes_power_log_differenced                 37.499663       208.081536            0.180           0.857
L3.total_raw_bytes_committed_log_differenced           -31.145809       210.098889           -0.148           0.882
L3.total_raw_bytes_power_log_differenced                70.658429       208.326014            0.339           0.734
L3.burnt_fil_log_differenced                           -13.554503         5.463514           -2.481           0.013
L3.circulating_fil_log_differenced                     -69.924483        27.807339           -2.515           0.012
L3.locked_fil_log_differenced                         -142.262979       428.456387           -0.332           0.740
L3.vested_fil_log_differenced                           50.710021        80.904223            0.627           0.531
L4.cum_sum_baseline_log_differenced                   1607.157038      1349.799032            1.191           0.234
L4.cum_sum_realized_log_differenced                     22.033104       164.553808            0.134           0.893
L4.effective_baseline_power_log_differenced           -769.731675       672.703643           -1.144           0.253
L4.effective_network_time_log_differenced            -1630.727903      1424.476883           -1.145           0.252
L4.new_baseline_power_log_differenced                 -137.693918       597.386562           -0.230           0.818
L4.total_mined_reward_log_differenced                   96.529090        14.960935            6.452           0.000
L4.miner_count_log_differenced                           0.492404         0.129110            3.814           0.000
L4.participating_miner_count_log_differenced             0.098292         0.031613            3.109           0.002
L4.qa_smoothed_position_estimate_log_differenced        -0.361163         0.074607           -4.841           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000284         0.000438            0.649           0.516
L4.total_pledge_collateral_log_differenced           -1312.202092       433.482822           -3.027           0.002
L4.total_qa_bytes_committed_log_differenced            153.772882       209.307256            0.735           0.463
L4.total_qa_bytes_power_log_differenced               -306.453502       207.618659           -1.476           0.140
L4.total_raw_bytes_committed_log_differenced           -99.151576       209.606647           -0.473           0.636
L4.total_raw_bytes_power_log_differenced               251.631429       207.886025            1.210           0.226
L4.burnt_fil_log_differenced                           -33.497454         5.469953           -6.124           0.000
L4.circulating_fil_log_differenced                    -173.179730        27.837995           -6.221           0.000
L4.locked_fil_log_differenced                         1210.373750       428.052636            2.828           0.005
L4.vested_fil_log_differenced                          210.733944        68.386129            3.082           0.002
===================================================================================================================

Results for equation total_mined_reward_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000012            0.009           0.993
L1.cum_sum_baseline_log_differenced                   9927.648368      3300.400166            3.008           0.003
L1.cum_sum_realized_log_differenced                    -85.876865       401.320544           -0.214           0.831
L1.effective_baseline_power_log_differenced          -5637.028637      1641.593743           -3.434           0.001
L1.effective_network_time_log_differenced            -9745.239470      3483.359511           -2.798           0.005
L1.new_baseline_power_log_differenced                   86.463562      1457.285965            0.059           0.953
L1.total_mined_reward_log_differenced                   82.845584        36.526093            2.268           0.023
L1.miner_count_log_differenced                           0.597692         0.314439            1.901           0.057
L1.participating_miner_count_log_differenced             0.633543         0.077134            8.213           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.438517         0.182466            2.403           0.016
L1.qa_smoothed_velocity_estimate_log_differenced        -0.003147         0.001069           -2.943           0.003
L1.total_pledge_collateral_log_differenced           -6379.872317      1055.230437           -6.046           0.000
L1.total_qa_bytes_committed_log_differenced          -2938.250229       511.117825           -5.749           0.000
L1.total_qa_bytes_power_log_differenced               2454.062288       507.073365            4.840           0.000
L1.total_raw_bytes_committed_log_differenced          3169.713129       512.037200            6.190           0.000
L1.total_raw_bytes_power_log_differenced             -2685.416860       507.909979           -5.287           0.000
L1.burnt_fil_log_differenced                           -23.236572        13.342419           -1.742           0.082
L1.circulating_fil_log_differenced                    -114.979617        67.911138           -1.693           0.090
L1.locked_fil_log_differenced                         6311.900882      1042.002841            6.057           0.000
L1.vested_fil_log_differenced                          156.610759       167.537202            0.935           0.350
L2.cum_sum_baseline_log_differenced                  23314.192428      3483.170892            6.693           0.000
L2.cum_sum_realized_log_differenced                     48.179653       430.786641            0.112           0.911
L2.effective_baseline_power_log_differenced         -12988.428335      1722.920460           -7.539           0.000
L2.effective_network_time_log_differenced           -23086.941957      3684.554529           -6.266           0.000
L2.new_baseline_power_log_differenced                 -247.239974      1570.946716           -0.157           0.875
L2.total_mined_reward_log_differenced                  -24.978179        36.486084           -0.685           0.494
L2.miner_count_log_differenced                           0.158030         0.314707            0.502           0.616
L2.participating_miner_count_log_differenced             0.271531         0.077129            3.520           0.000
L2.qa_smoothed_position_estimate_log_differenced         0.818512         0.182143            4.494           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.000933         0.001090            0.856           0.392
L2.total_pledge_collateral_log_differenced           -4947.878176      1058.103865           -4.676           0.000
L2.total_qa_bytes_committed_log_differenced          -2361.061901       511.971538           -4.612           0.000
L2.total_qa_bytes_power_log_differenced               1935.367872       507.705325            3.812           0.000
L2.total_raw_bytes_committed_log_differenced          2273.335052       512.681273            4.434           0.000
L2.total_raw_bytes_power_log_differenced             -1848.337322       508.338680           -3.636           0.000
L2.burnt_fil_log_differenced                            19.376731        13.331174            1.453           0.146
L2.circulating_fil_log_differenced                      83.742666        67.851170            1.234           0.217
L2.locked_fil_log_differenced                         5003.165454      1044.908582            4.788           0.000
L2.vested_fil_log_differenced                          -98.026378       197.438179           -0.496           0.620
L3.cum_sum_baseline_log_differenced                   2121.032102      3480.040886            0.609           0.542
L3.cum_sum_realized_log_differenced                      8.663706       430.663704            0.020           0.984
L3.effective_baseline_power_log_differenced          -1155.433014      1724.017250           -0.670           0.503
L3.effective_network_time_log_differenced            -2088.858721      3680.613933           -0.568           0.570
L3.new_baseline_power_log_differenced                   40.488302      1570.318093            0.026           0.979
L3.total_mined_reward_log_differenced                   72.160246        36.459314            1.979           0.048
L3.miner_count_log_differenced                           0.425511         0.314872            1.351           0.177
L3.participating_miner_count_log_differenced            -0.065687         0.077137           -0.852           0.394
L3.qa_smoothed_position_estimate_log_differenced        -0.286377         0.182146           -1.572           0.116
L3.qa_smoothed_velocity_estimate_log_differenced         0.002386         0.001090            2.189           0.029
L3.total_pledge_collateral_log_differenced             182.372991      1058.039935            0.172           0.863
L3.total_qa_bytes_committed_log_differenced           -130.673541       511.676360           -0.255           0.798
L3.total_qa_bytes_power_log_differenced                 30.647000       507.429731            0.060           0.952
L3.total_raw_bytes_committed_log_differenced          -131.019192       512.349268           -0.256           0.798
L3.total_raw_bytes_power_log_differenced               231.461360       508.025917            0.456           0.649
L3.burnt_fil_log_differenced                           -33.268914        13.323380           -2.497           0.013
L3.circulating_fil_log_differenced                    -171.500049        67.811258           -2.529           0.011
L3.locked_fil_log_differenced                         -283.574374      1044.838063           -0.271           0.786
L3.vested_fil_log_differenced                          124.351466       197.293854            0.630           0.529
L4.cum_sum_baseline_log_differenced                   3754.407102      3291.633523            1.141           0.254
L4.cum_sum_realized_log_differenced                     62.128501       401.282574            0.155           0.877
L4.effective_baseline_power_log_differenced          -1762.440168      1640.461884           -1.074           0.283
L4.effective_network_time_log_differenced            -3822.343033      3473.743683           -1.100           0.271
L4.new_baseline_power_log_differenced                 -361.219178      1456.792890           -0.248           0.804
L4.total_mined_reward_log_differenced                  236.448270        36.483887            6.481           0.000
L4.miner_count_log_differenced                           1.200396         0.314849            3.813           0.000
L4.participating_miner_count_log_differenced             0.237785         0.077091            3.084           0.002
L4.qa_smoothed_position_estimate_log_differenced        -0.880720         0.181936           -4.841           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000697         0.001067            0.653           0.514
L4.total_pledge_collateral_log_differenced           -3251.687396      1057.095579           -3.076           0.002
L4.total_qa_bytes_committed_log_differenced            387.355292       510.418784            0.759           0.448
L4.total_qa_bytes_power_log_differenced               -763.960010       506.300954           -1.509           0.131
L4.total_raw_bytes_committed_log_differenced          -251.786393       511.148882           -0.493           0.622
L4.total_raw_bytes_power_log_differenced               627.895324       506.952956            1.239           0.216
L4.burnt_fil_log_differenced                           -81.961569        13.339082           -6.144           0.000
L4.circulating_fil_log_differenced                    -423.538221        67.886015           -6.239           0.000
L4.locked_fil_log_differenced                         3002.549789      1043.853472            2.876           0.004
L4.vested_fil_log_differenced                          510.471994       166.767104            3.061           0.002
===================================================================================================================

Results for equation miner_count_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000001            0.006           0.996
L1.cum_sum_baseline_log_differenced                   1332.897832       212.989078            6.258           0.000
L1.cum_sum_realized_log_differenced                     29.018455        25.898948            1.120           0.263
L1.effective_baseline_power_log_differenced           -658.584846       105.939135           -6.217           0.000
L1.effective_network_time_log_differenced            -1349.851363       224.796235           -6.005           0.000
L1.new_baseline_power_log_differenced                 -131.171569        94.044958           -1.395           0.163
L1.total_mined_reward_log_differenced                    2.293139         2.357187            0.973           0.331
L1.miner_count_log_differenced                          -0.016992         0.020292           -0.837           0.402
L1.participating_miner_count_log_differenced             0.038961         0.004978            7.827           0.000
L1.qa_smoothed_position_estimate_log_differenced        -0.026323         0.011775           -2.235           0.025
L1.qa_smoothed_velocity_estimate_log_differenced        -0.000063         0.000069           -0.916           0.360
L1.total_pledge_collateral_log_differenced            -458.376660        68.098578           -6.731           0.000
L1.total_qa_bytes_committed_log_differenced           -289.485904        32.984641           -8.776           0.000
L1.total_qa_bytes_power_log_differenced                268.394775        32.723634            8.202           0.000
L1.total_raw_bytes_committed_log_differenced           300.257152        33.043972            9.087           0.000
L1.total_raw_bytes_power_log_differenced              -279.101830        32.777625           -8.515           0.000
L1.burnt_fil_log_differenced                            -0.526589         0.861044           -0.612           0.541
L1.circulating_fil_log_differenced                      -2.549285         4.382599           -0.582           0.561
L1.locked_fil_log_differenced                          457.001047        67.244944            6.796           0.000
L1.vested_fil_log_differenced                           13.185574        10.811899            1.220           0.223
L2.cum_sum_baseline_log_differenced                   1817.381245       224.784063            8.085           0.000
L2.cum_sum_realized_log_differenced                     21.096029        27.800523            0.759           0.448
L2.effective_baseline_power_log_differenced           -966.364820       111.187499           -8.691           0.000
L2.effective_network_time_log_differenced            -1817.474038       237.780219           -7.644           0.000
L2.new_baseline_power_log_differenced                  -78.558208       101.379977           -0.775           0.438
L2.total_mined_reward_log_differenced                   -0.086521         2.354605           -0.037           0.971
L2.miner_count_log_differenced                          -0.058312         0.020309           -2.871           0.004
L2.participating_miner_count_log_differenced             0.018435         0.004977            3.704           0.000
L2.qa_smoothed_position_estimate_log_differenced         0.066155         0.011754            5.628           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.000064         0.000070            0.916           0.360
L2.total_pledge_collateral_log_differenced            -285.499579        68.284013           -4.181           0.000
L2.total_qa_bytes_committed_log_differenced           -170.688695        33.039735           -5.166           0.000
L2.total_qa_bytes_power_log_differenced                153.828809        32.764418            4.695           0.000
L2.total_raw_bytes_committed_log_differenced           169.528585        33.085537            5.124           0.000
L2.total_raw_bytes_power_log_differenced              -152.732798        32.805291           -4.656           0.000
L2.burnt_fil_log_differenced                             0.788915         0.860318            0.917           0.359
L2.circulating_fil_log_differenced                       2.812123         4.378729            0.642           0.521
L2.locked_fil_log_differenced                          287.504631        67.432464            4.264           0.000
L2.vested_fil_log_differenced                           -6.621438        12.741539           -0.520           0.603
L3.cum_sum_baseline_log_differenced                    296.664322       224.582070            1.321           0.187
L3.cum_sum_realized_log_differenced                    -18.798515        27.792589           -0.676           0.499
L3.effective_baseline_power_log_differenced           -220.914318       111.258280           -1.986           0.047
L3.effective_network_time_log_differenced             -271.901535       237.525915           -1.145           0.252
L3.new_baseline_power_log_differenced                   75.946090       101.339409            0.749           0.454
L3.total_mined_reward_log_differenced                    4.072940         2.352877            1.731           0.083
L3.miner_count_log_differenced                          -0.005993         0.020320           -0.295           0.768
L3.participating_miner_count_log_differenced            -0.010907         0.004978           -2.191           0.028
L3.qa_smoothed_position_estimate_log_differenced        -0.044868         0.011755           -3.817           0.000
L3.qa_smoothed_velocity_estimate_log_differenced         0.000084         0.000070            1.188           0.235
L3.total_pledge_collateral_log_differenced              43.455206        68.279887            0.636           0.524
L3.total_qa_bytes_committed_log_differenced           -114.084532        33.020686           -3.455           0.001
L3.total_qa_bytes_power_log_differenced                111.778406        32.746632            3.413           0.001
L3.total_raw_bytes_committed_log_differenced           100.438951        33.064111            3.038           0.002
L3.total_raw_bytes_power_log_differenced               -98.074658        32.785107           -2.991           0.003
L3.burnt_fil_log_differenced                            -2.137068         0.859815           -2.485           0.013
L3.circulating_fil_log_differenced                     -11.159240         4.376153           -2.550           0.011
L3.locked_fil_log_differenced                          -49.966111        67.427913           -0.741           0.459
L3.vested_fil_log_differenced                           10.144475        12.732225            0.797           0.426
L4.cum_sum_baseline_log_differenced                    514.865676       212.423329            2.424           0.015
L4.cum_sum_realized_log_differenced                      3.923734        25.896498            0.152           0.880
L4.effective_baseline_power_log_differenced           -267.358042       105.866091           -2.525           0.012
L4.effective_network_time_log_differenced             -516.063526       224.175684           -2.302           0.021
L4.new_baseline_power_log_differenced                  -30.276115        94.013138           -0.322           0.747
L4.total_mined_reward_log_differenced                   10.279746         2.354463            4.366           0.000
L4.miner_count_log_differenced                           0.065753         0.020319            3.236           0.001
L4.participating_miner_count_log_differenced             0.013585         0.004975            2.731           0.006
L4.qa_smoothed_position_estimate_log_differenced        -0.060218         0.011741           -5.129           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000044         0.000069            0.634           0.526
L4.total_pledge_collateral_log_differenced            -105.123697        68.218944           -1.541           0.123
L4.total_qa_bytes_committed_log_differenced            -21.986283        32.939529           -0.667           0.504
L4.total_qa_bytes_power_log_differenced                  4.489510        32.673787            0.137           0.891
L4.total_raw_bytes_committed_log_differenced            26.828082        32.986645            0.813           0.416
L4.total_raw_bytes_power_log_differenced                -9.332493        32.715864           -0.285           0.775
L4.burnt_fil_log_differenced                            -3.634212         0.860829           -4.222           0.000
L4.circulating_fil_log_differenced                     -19.101411         4.380978           -4.360           0.000
L4.locked_fil_log_differenced                           94.133078        67.364373            1.397           0.162
L4.vested_fil_log_differenced                           30.295369        10.762202            2.815           0.005
===================================================================================================================

Results for equation participating_miner_count_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000006            0.010           0.992
L1.cum_sum_baseline_log_differenced                   3717.383132      1694.890414            2.193           0.028
L1.cum_sum_realized_log_differenced                    -98.895967       206.094507           -0.480           0.631
L1.effective_baseline_power_log_differenced          -2264.572053       843.025500           -2.686           0.007
L1.effective_network_time_log_differenced            -3582.545363      1788.847518           -2.003           0.045
L1.new_baseline_power_log_differenced                  258.034688       748.375921            0.345           0.730
L1.total_mined_reward_log_differenced                   52.894603        18.757642            2.820           0.005
L1.miner_count_log_differenced                           0.421069         0.161477            2.608           0.009
L1.participating_miner_count_log_differenced             0.296257         0.039612            7.479           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.307094         0.093704            3.277           0.001
L1.qa_smoothed_velocity_estimate_log_differenced        -0.001714         0.000549           -3.122           0.002
L1.total_pledge_collateral_log_differenced           -3361.910260       541.903970           -6.204           0.000
L1.total_qa_bytes_committed_log_differenced          -1356.734365       262.479899           -5.169           0.000
L1.total_qa_bytes_power_log_differenced               1099.708089       260.402903            4.223           0.000
L1.total_raw_bytes_committed_log_differenced          1488.235665       262.952036            5.660           0.000
L1.total_raw_bytes_power_log_differenced             -1231.249544       260.832539           -4.720           0.000
L1.burnt_fil_log_differenced                           -15.479714         6.851878           -2.259           0.024
L1.circulating_fil_log_differenced                     -76.525442        34.875146           -2.194           0.028
L1.locked_fil_log_differenced                         3316.170848       535.111059            6.197           0.000
L1.vested_fil_log_differenced                           88.398880        86.037202            1.027           0.304
L2.cum_sum_baseline_log_differenced                  10975.427980      1788.750654            6.136           0.000
L2.cum_sum_realized_log_differenced                     12.068942       221.226552            0.055           0.956
L2.effective_baseline_power_log_differenced          -6156.755272       884.790094           -6.958           0.000
L2.effective_network_time_log_differenced           -10851.683389      1892.169385           -5.735           0.000
L2.new_baseline_power_log_differenced                  -45.029592       806.745363           -0.056           0.955
L2.total_mined_reward_log_differenced                  -19.541913        18.737096           -1.043           0.297
L2.miner_count_log_differenced                           0.146559         0.161615            0.907           0.364
L2.participating_miner_count_log_differenced             0.106021         0.039609            2.677           0.007
L2.qa_smoothed_position_estimate_log_differenced         0.421132         0.093538            4.502           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.000560         0.000560            1.000           0.317
L2.total_pledge_collateral_log_differenced           -2710.574503       543.379593           -4.988           0.000
L2.total_qa_bytes_committed_log_differenced          -1143.644598       262.918315           -4.350           0.000
L2.total_qa_bytes_power_log_differenced                912.990766       260.727441            3.502           0.000
L2.total_raw_bytes_committed_log_differenced          1104.735023       263.282793            4.196           0.000
L2.total_raw_bytes_power_log_differenced              -874.426147       261.052695           -3.350           0.001
L2.burnt_fil_log_differenced                            11.966149         6.846103            1.748           0.080
L2.circulating_fil_log_differenced                      54.195545        34.844350            1.555           0.120
L2.locked_fil_log_differenced                         2745.537173       536.603275            5.117           0.000
L2.vested_fil_log_differenced                          -89.726308       101.392577           -0.885           0.376
L3.cum_sum_baseline_log_differenced                    -22.185461      1787.143268           -0.012           0.990
L3.cum_sum_realized_log_differenced                      7.975540       221.163419            0.036           0.971
L3.effective_baseline_power_log_differenced             48.818092       885.353340            0.055           0.956
L3.effective_network_time_log_differenced               20.688573      1890.145728            0.011           0.991
L3.new_baseline_power_log_differenced                   18.335109       806.422539            0.023           0.982
L3.total_mined_reward_log_differenced                   55.506961        18.723348            2.965           0.003
L3.miner_count_log_differenced                           0.331471         0.161700            2.050           0.040
L3.participating_miner_count_log_differenced            -0.064271         0.039613           -1.622           0.105
L3.qa_smoothed_position_estimate_log_differenced        -0.096842         0.093540           -1.035           0.301
L3.qa_smoothed_velocity_estimate_log_differenced         0.001131         0.000560            2.019           0.043
L3.total_pledge_collateral_log_differenced            -180.379678       543.346762           -0.332           0.740
L3.total_qa_bytes_committed_log_differenced            137.281298       262.766730            0.522           0.601
L3.total_qa_bytes_power_log_differenced               -198.772020       260.585912           -0.763           0.446
L3.total_raw_bytes_committed_log_differenced          -270.610654       263.112296           -1.028           0.304
L3.total_raw_bytes_power_log_differenced               332.254137       260.892078            1.274           0.203
L3.burnt_fil_log_differenced                           -23.560249         6.842100           -3.443           0.001
L3.circulating_fil_log_differenced                    -120.530780        34.823853           -3.461           0.001
L3.locked_fil_log_differenced                          108.425243       536.567061            0.202           0.840
L3.vested_fil_log_differenced                           87.911417       101.318460            0.868           0.386
L4.cum_sum_baseline_log_differenced                   1303.083398      1690.388385            0.771           0.441
L4.cum_sum_realized_log_differenced                     24.818281       206.075007            0.120           0.904
L4.effective_baseline_power_log_differenced           -572.280378       842.444244           -0.679           0.497
L4.effective_network_time_log_differenced            -1337.767644      1783.909397           -0.750           0.453
L4.new_baseline_power_log_differenced                 -151.162315       748.122706           -0.202           0.840
L4.total_mined_reward_log_differenced                  126.231382        18.735967            6.737           0.000
L4.miner_count_log_differenced                           0.623763         0.161688            3.858           0.000
L4.participating_miner_count_log_differenced             0.094209         0.039589            2.380           0.017
L4.qa_smoothed_position_estimate_log_differenced        -0.395931         0.093432           -4.238           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000405         0.000548            0.738           0.460
L4.total_pledge_collateral_log_differenced           -1706.919395       542.861797           -3.144           0.002
L4.total_qa_bytes_committed_log_differenced            362.397043       262.120913            1.383           0.167
L4.total_qa_bytes_power_log_differenced               -562.596822       260.006239           -2.164           0.030
L4.total_raw_bytes_committed_log_differenced          -291.526765       262.495848           -1.111           0.267
L4.total_raw_bytes_power_log_differenced               491.432939       260.341069            1.888           0.059
L4.burnt_fil_log_differenced                           -43.835254         6.850164           -6.399           0.000
L4.circulating_fil_log_differenced                    -226.095915        34.862244           -6.485           0.000
L4.locked_fil_log_differenced                         1573.685156       536.061433            2.936           0.003
L4.vested_fil_log_differenced                          264.755343        85.641726            3.091           0.002
===================================================================================================================

Results for equation qa_smoothed_position_estimate_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000013            0.009           0.993
L1.cum_sum_baseline_log_differenced                  10339.223174      3783.773587            2.733           0.006
L1.cum_sum_realized_log_differenced                   -144.088610       460.097564           -0.313           0.754
L1.effective_baseline_power_log_differenced          -6003.904448      1882.019977           -3.190           0.001
L1.effective_network_time_log_differenced           -10092.345550      3993.528981           -2.527           0.011
L1.new_baseline_power_log_differenced                  281.301487      1670.718660            0.168           0.866
L1.total_mined_reward_log_differenced                   91.390306        41.875669            2.182           0.029
L1.miner_count_log_differenced                           0.729173         0.360492            2.023           0.043
L1.participating_miner_count_log_differenced             0.721484         0.088432            8.159           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.540606         0.209190            2.584           0.010
L1.qa_smoothed_velocity_estimate_log_differenced        -0.003603         0.001226           -2.939           0.003
L1.total_pledge_collateral_log_differenced           -7041.734458      1209.778467           -5.821           0.000
L1.total_qa_bytes_committed_log_differenced          -3260.714939       585.975648           -5.565           0.000
L1.total_qa_bytes_power_log_differenced               2708.292808       581.338840            4.659           0.000
L1.total_raw_bytes_committed_log_differenced          3527.999067       587.029674            6.010           0.000
L1.total_raw_bytes_power_log_differenced             -2975.494013       582.297984           -5.110           0.000
L1.burnt_fil_log_differenced                           -25.598822        15.296537           -1.674           0.094
L1.circulating_fil_log_differenced                    -126.229159        77.857338           -1.621           0.105
L1.locked_fil_log_differenced                         6967.331482      1194.613571            5.832           0.000
L1.vested_fil_log_differenced                          161.752217       192.074539            0.842           0.400
L2.cum_sum_baseline_log_differenced                  26045.475411      3993.312737            6.522           0.000
L2.cum_sum_realized_log_differenced                      8.806063       493.879237            0.018           0.986
L2.effective_baseline_power_log_differenced         -14628.493146      1975.257727           -7.406           0.000
L2.effective_network_time_log_differenced           -25744.239080      4224.190827           -6.094           0.000
L2.new_baseline_power_log_differenced                 -113.355711      1801.026055           -0.063           0.950
L2.total_mined_reward_log_differenced                  -25.472071        41.829800           -0.609           0.543
L2.miner_count_log_differenced                           0.197671         0.360798            0.548           0.584
L2.participating_miner_count_log_differenced             0.310905         0.088426            3.516           0.000
L2.qa_smoothed_position_estimate_log_differenced         0.909979         0.208820            4.358           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.001020         0.001250            0.816           0.414
L2.total_pledge_collateral_log_differenced           -5606.243716      1213.072735           -4.622           0.000
L2.total_qa_bytes_committed_log_differenced          -2692.216262       586.954394           -4.587           0.000
L2.total_qa_bytes_power_log_differenced               2204.143314       582.063356            3.787           0.000
L2.total_raw_bytes_committed_log_differenced          2592.534080       587.768077            4.411           0.000
L2.total_raw_bytes_power_log_differenced             -2105.226593       582.789473           -3.612           0.000
L2.burnt_fil_log_differenced                            20.859810        15.283645            1.365           0.172
L2.circulating_fil_log_differenced                      89.426627        77.788587            1.150           0.250
L2.locked_fil_log_differenced                         5665.590072      1197.944884            4.729           0.000
L2.vested_fil_log_differenced                         -106.659153       226.354784           -0.471           0.637
L3.cum_sum_baseline_log_differenced                   2586.066530      3989.724314            0.648           0.517
L3.cum_sum_realized_log_differenced                     -2.483664       493.738294           -0.005           0.996
L3.effective_baseline_power_log_differenced          -1441.986222      1976.515152           -0.730           0.466
L3.effective_network_time_log_differenced            -2534.009393      4219.673095           -0.601           0.548
L3.new_baseline_power_log_differenced                   90.114387      1800.305364            0.050           0.960
L3.total_mined_reward_log_differenced                   82.131450        41.799109            1.965           0.049
L3.miner_count_log_differenced                           0.491203         0.360988            1.361           0.174
L3.participating_miner_count_log_differenced            -0.064377         0.088435           -0.728           0.467
L3.qa_smoothed_position_estimate_log_differenced        -0.303517         0.208823           -1.453           0.146
L3.qa_smoothed_velocity_estimate_log_differenced         0.002676         0.001250            2.141           0.032
L3.total_pledge_collateral_log_differenced             164.999620      1212.999443            0.136           0.892
L3.total_qa_bytes_committed_log_differenced           -132.026995       586.615986           -0.225           0.822
L3.total_qa_bytes_power_log_differenced                 15.732529       581.747399            0.027           0.978
L3.total_raw_bytes_committed_log_differenced          -164.136180       587.387448           -0.279           0.780
L3.total_raw_bytes_power_log_differenced               280.879011       582.430902            0.482           0.630
L3.burnt_fil_log_differenced                           -37.741709        15.274709           -2.471           0.013
L3.circulating_fil_log_differenced                    -194.705260        77.742829           -2.504           0.012
L3.locked_fil_log_differenced                         -279.722731      1197.864037           -0.234           0.815
L3.vested_fil_log_differenced                          137.129293       226.189321            0.606           0.544
L4.cum_sum_baseline_log_differenced                   3985.318658      3773.722990            1.056           0.291
L4.cum_sum_realized_log_differenced                     47.920640       460.054032            0.104           0.917
L4.effective_baseline_power_log_differenced          -1906.035807      1880.722347           -1.013           0.311
L4.effective_network_time_log_differenced            -4040.150011      3982.504828           -1.014           0.310
L4.new_baseline_power_log_differenced                 -316.338725      1670.153370           -0.189           0.850
L4.total_mined_reward_log_differenced                  270.963088        41.827282            6.478           0.000
L4.miner_count_log_differenced                           1.357276         0.360962            3.760           0.000
L4.participating_miner_count_log_differenced             0.263883         0.088381            2.986           0.003
L4.qa_smoothed_position_estimate_log_differenced        -1.037812         0.208583           -4.976           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000821         0.001223            0.671           0.502
L4.total_pledge_collateral_log_differenced           -3732.448907      1211.916777           -3.080           0.002
L4.total_qa_bytes_committed_log_differenced            425.859444       585.174226            0.728           0.467
L4.total_qa_bytes_power_log_differenced               -855.906734       580.453302           -1.475           0.140
L4.total_raw_bytes_committed_log_differenced          -269.431176       586.011253           -0.460           0.646
L4.total_raw_bytes_power_log_differenced               698.912689       581.200797            1.203           0.229
L4.burnt_fil_log_differenced                           -93.992349        15.292711           -6.146           0.000
L4.circulating_fil_log_differenced                    -485.491780        77.828535           -6.238           0.000
L4.locked_fil_log_differenced                         3446.834652      1196.735243            2.880           0.004
L4.vested_fil_log_differenced                          572.089295       191.191653            2.992           0.003
===================================================================================================================

Results for equation qa_smoothed_velocity_estimate_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                   -0.000008         0.000062           -0.131           0.895
L1.cum_sum_baseline_log_differenced                -155007.117702     17432.147819           -8.892           0.000
L1.cum_sum_realized_log_differenced                    277.480313      2119.706309            0.131           0.896
L1.effective_baseline_power_log_differenced          87682.672747      8670.616699           10.113           0.000
L1.effective_network_time_log_differenced           152833.324607     18398.507712            8.307           0.000
L1.new_baseline_power_log_differenced                  456.417029      7697.134615            0.059           0.953
L1.total_mined_reward_log_differenced                  143.678566       192.924561            0.745           0.456
L1.miner_count_log_differenced                           3.740017         1.660815            2.252           0.024
L1.participating_miner_count_log_differenced             0.783090         0.407411            1.922           0.055
L1.qa_smoothed_position_estimate_log_differenced         0.493463         0.963755            0.512           0.609
L1.qa_smoothed_velocity_estimate_log_differenced         0.225239         0.005648           39.882           0.000
L1.total_pledge_collateral_log_differenced           77868.571563      5573.546247           13.971           0.000
L1.total_qa_bytes_committed_log_differenced          34877.176566      2699.636722           12.919           0.000
L1.total_qa_bytes_power_log_differenced             -31146.809109      2678.274574          -11.629           0.000
L1.total_raw_bytes_committed_log_differenced        -34866.572382      2704.492702          -12.892           0.000
L1.total_raw_bytes_power_log_differenced             31127.140491      2682.693426           11.603           0.000
L1.burnt_fil_log_differenced                           -45.383659        70.472369           -0.644           0.520
L1.circulating_fil_log_differenced                    -188.857033       358.694989           -0.527           0.599
L1.locked_fil_log_differenced                       -77949.634361      5503.680354          -14.163           0.000
L1.vested_fil_log_differenced                         -630.341877       884.902775           -0.712           0.476
L2.cum_sum_baseline_log_differenced                -124218.069826     18397.511461           -6.752           0.000
L2.cum_sum_realized_log_differenced                   -584.416176      2275.341181           -0.257           0.797
L2.effective_baseline_power_log_differenced          68675.946525      9100.170474            7.547           0.000
L2.effective_network_time_log_differenced           123154.856282     19461.185305            6.328           0.000
L2.new_baseline_power_log_differenced                 2885.781131      8297.471216            0.348           0.728
L2.total_mined_reward_log_differenced                 1593.663858       192.713239            8.270           0.000
L2.miner_count_log_differenced                          -2.321861         1.662227           -1.397           0.162
L2.participating_miner_count_log_differenced            -0.031877         0.407384           -0.078           0.938
L2.qa_smoothed_position_estimate_log_differenced        -6.549872         0.962050           -6.808           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.088736         0.005759           15.409           0.000
L2.total_pledge_collateral_log_differenced           34765.515758      5588.723202            6.221           0.000
L2.total_qa_bytes_committed_log_differenced          18823.373284      2704.145883            6.961           0.000
L2.total_qa_bytes_power_log_differenced             -16398.368432      2681.612479           -6.115           0.000
L2.total_raw_bytes_committed_log_differenced        -18489.250839      2707.894585           -6.828           0.000
L2.total_raw_bytes_power_log_differenced             16067.469033      2684.957755            5.984           0.000
L2.burnt_fil_log_differenced                          -596.209520        70.412976           -8.467           0.000
L2.circulating_fil_log_differenced                   -2992.828369       358.378247           -8.351           0.000
L2.locked_fil_log_differenced                       -36585.352746      5519.027979           -6.629           0.000
L2.vested_fil_log_differenced                         3113.163757      1042.834612            2.985           0.003
L3.cum_sum_baseline_log_differenced                 -19068.889406     18380.979306           -1.037           0.300
L3.cum_sum_realized_log_differenced                   1063.219106      2274.691847            0.467           0.640
L3.effective_baseline_power_log_differenced          13734.516498      9105.963531            1.508           0.131
L3.effective_network_time_log_differenced            17481.328304     19440.371751            0.899           0.369
L3.new_baseline_power_log_differenced                -4424.683220      8294.150936           -0.533           0.594
L3.total_mined_reward_log_differenced                   69.149651       192.571843            0.359           0.720
L3.miner_count_log_differenced                          -0.219964         1.663099           -0.132           0.895
L3.participating_miner_count_log_differenced             1.374882         0.407427            3.375           0.001
L3.qa_smoothed_position_estimate_log_differenced         2.361986         0.962066            2.455           0.014
L3.qa_smoothed_velocity_estimate_log_differenced         0.048776         0.005759            8.470           0.000
L3.total_pledge_collateral_log_differenced            2473.959221      5588.385537            0.443           0.658
L3.total_qa_bytes_committed_log_differenced           3148.397645      2702.586809            1.165           0.244
L3.total_qa_bytes_power_log_differenced              -2419.926706      2680.156838           -0.903           0.367
L3.total_raw_bytes_committed_log_differenced         -1549.996179      2706.140994           -0.573           0.567
L3.total_raw_bytes_power_log_differenced               815.716248      2683.305794            0.304           0.761
L3.burnt_fil_log_differenced                            14.750322        70.371806            0.210           0.834
L3.circulating_fil_log_differenced                     104.331876       358.167437            0.291           0.771
L3.locked_fil_log_differenced                        -2392.322925      5518.655512           -0.433           0.665
L3.vested_fil_log_differenced                          490.535805      1042.072309            0.471           0.638
L4.cum_sum_baseline_log_differenced                  -1768.135401     17385.843917           -0.102           0.919
L4.cum_sum_realized_log_differenced                    987.398625      2119.505756            0.466           0.641
L4.effective_baseline_power_log_differenced           3643.067623      8664.638413            0.420           0.674
L4.effective_network_time_log_differenced              622.431463     18347.718557            0.034           0.973
L4.new_baseline_power_log_differenced                -3526.940221      7694.530276           -0.458           0.647
L4.total_mined_reward_log_differenced                  378.822204       192.701634            1.966           0.049
L4.miner_count_log_differenced                          -5.101466         1.662980           -3.068           0.002
L4.participating_miner_count_log_differenced            -0.186650         0.407179           -0.458           0.647
L4.qa_smoothed_position_estimate_log_differenced         9.194079         0.960956            9.568           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.048930         0.005636            8.681           0.000
L4.total_pledge_collateral_log_differenced           26497.072053      5583.397609            4.746           0.000
L4.total_qa_bytes_committed_log_differenced           7183.619151      2695.944504            2.665           0.008
L4.total_qa_bytes_power_log_differenced              -5089.896113      2674.194831           -1.903           0.057
L4.total_raw_bytes_committed_log_differenced         -8196.500851      2699.800757           -3.036           0.002
L4.total_raw_bytes_power_log_differenced              6103.265085      2677.638597            2.279           0.023
L4.burnt_fil_log_differenced                          -129.444963        70.454745           -1.837           0.066
L4.circulating_fil_log_differenced                    -677.924499       358.562291           -1.891           0.059
L4.locked_fil_log_differenced                       -26910.947725      5513.455068           -4.881           0.000
L4.vested_fil_log_differenced                          894.247627       880.835249            1.015           0.310
===================================================================================================================

Results for equation total_pledge_collateral_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000008            0.009           0.993
L1.cum_sum_baseline_log_differenced                   6781.887100      2365.355914            2.867           0.004
L1.cum_sum_realized_log_differenced                    -73.209279       287.621463           -0.255           0.799
L1.effective_baseline_power_log_differenced          -3884.710320      1176.509900           -3.302           0.001
L1.effective_network_time_log_differenced            -6642.457340      2496.480610           -2.661           0.008
L1.new_baseline_power_log_differenced                  110.493987      1044.418798            0.106           0.916
L1.total_mined_reward_log_differenced                   61.084097        26.177798            2.333           0.020
L1.miner_count_log_differenced                           0.436929         0.225355            1.939           0.053
L1.participating_miner_count_log_differenced             0.446225         0.055281            8.072           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.334928         0.130771            2.561           0.010
L1.qa_smoothed_velocity_estimate_log_differenced        -0.002329         0.000766           -3.039           0.002
L1.total_pledge_collateral_log_differenced           -4566.025846       756.270582           -6.038           0.000
L1.total_qa_bytes_committed_log_differenced          -2047.605459       366.311814           -5.590           0.000
L1.total_qa_bytes_power_log_differenced               1692.993371       363.413199            4.659           0.000
L1.total_raw_bytes_committed_log_differenced          2212.606292       366.970718            6.029           0.000
L1.total_raw_bytes_power_log_differenced             -1857.937781       364.012790           -5.104           0.000
L1.burnt_fil_log_differenced                           -17.158998         9.562346           -1.794           0.073
L1.circulating_fil_log_differenced                     -85.005919        48.671072           -1.747           0.081
L1.locked_fil_log_differenced                         4515.613190       746.790528            6.047           0.000
L1.vested_fil_log_differenced                          110.045445       120.071837            0.916           0.359
L2.cum_sum_baseline_log_differenced                  16337.922943      2496.345429            6.545           0.000
L2.cum_sum_realized_log_differenced                     28.846328       308.739449            0.093           0.926
L2.effective_baseline_power_log_differenced          -9113.996494      1234.795750           -7.381           0.000
L2.effective_network_time_log_differenced           -16173.858627      2640.674587           -6.125           0.000
L2.new_baseline_power_log_differenced                 -157.726197      1125.878051           -0.140           0.889
L2.total_mined_reward_log_differenced                  -18.155900        26.149124           -0.694           0.487
L2.miner_count_log_differenced                           0.136630         0.225546            0.606           0.545
L2.participating_miner_count_log_differenced             0.192512         0.055278            3.483           0.000
L2.qa_smoothed_position_estimate_log_differenced         0.576933         0.130540            4.420           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.000654         0.000781            0.836           0.403
L2.total_pledge_collateral_log_differenced           -3565.994530       758.329932           -4.702           0.000
L2.total_qa_bytes_committed_log_differenced          -1678.612049       366.923659           -4.575           0.000
L2.total_qa_bytes_power_log_differenced               1367.294228       363.866117            3.758           0.000
L2.total_raw_bytes_committed_log_differenced          1616.101944       367.432317            4.398           0.000
L2.total_raw_bytes_power_log_differenced             -1305.269330       364.320035           -3.583           0.000
L2.burnt_fil_log_differenced                            13.944198         9.554287            1.459           0.144
L2.circulating_fil_log_differenced                      60.650146        48.628093            1.247           0.212
L2.locked_fil_log_differenced                         3605.907724       748.873036            4.815           0.000
L2.vested_fil_log_differenced                          -70.081911       141.501497           -0.495           0.620
L3.cum_sum_baseline_log_differenced                   1429.184707      2494.102193            0.573           0.567
L3.cum_sum_realized_log_differenced                     14.485718       308.651342            0.047           0.963
L3.effective_baseline_power_log_differenced           -752.029186      1235.581806           -0.609           0.543
L3.effective_network_time_log_differenced            -1416.362503      2637.850411           -0.537           0.591
L3.new_baseline_power_log_differenced                   -3.866671      1125.427524           -0.003           0.997
L3.total_mined_reward_log_differenced                   51.703486        26.129938            1.979           0.048
L3.miner_count_log_differenced                           0.303918         0.225665            1.347           0.178
L3.participating_miner_count_log_differenced            -0.040954         0.055283           -0.741           0.459
L3.qa_smoothed_position_estimate_log_differenced        -0.188906         0.130542           -1.447           0.148
L3.qa_smoothed_velocity_estimate_log_differenced         0.001724         0.000781            2.206           0.027
L3.total_pledge_collateral_log_differenced              88.935022       758.284115            0.117           0.907
L3.total_qa_bytes_committed_log_differenced            -37.386282       366.712109           -0.102           0.919
L3.total_qa_bytes_power_log_differenced                -37.492059       363.668602           -0.103           0.918
L3.total_raw_bytes_committed_log_differenced          -148.539692       367.194374           -0.405           0.686
L3.total_raw_bytes_power_log_differenced               223.697257       364.095882            0.614           0.539
L3.burnt_fil_log_differenced                           -23.646926         9.548701           -2.476           0.013
L3.circulating_fil_log_differenced                    -121.800450        48.599488           -2.506           0.012
L3.locked_fil_log_differenced                         -160.886741       748.822497           -0.215           0.830
L3.vested_fil_log_differenced                           87.587766       141.398061            0.619           0.536
L4.cum_sum_baseline_log_differenced                   2509.514454      2359.072970            1.064           0.287
L4.cum_sum_realized_log_differenced                     51.605262       287.594250            0.179           0.858
L4.effective_baseline_power_log_differenced          -1142.431043      1175.698710           -0.972           0.331
L4.effective_network_time_log_differenced            -2567.591154      2489.589065           -1.031           0.302
L4.new_baseline_power_log_differenced                 -280.471845      1044.065418           -0.269           0.788
L4.total_mined_reward_log_differenced                  170.549332        26.147550            6.523           0.000
L4.miner_count_log_differenced                           0.858130         0.225649            3.803           0.000
L4.participating_miner_count_log_differenced             0.169092         0.055250            3.061           0.002
L4.qa_smoothed_position_estimate_log_differenced        -0.626254         0.130392           -4.803           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000497         0.000765            0.650           0.516
L4.total_pledge_collateral_log_differenced           -2379.154881       757.607306           -3.140           0.002
L4.total_qa_bytes_committed_log_differenced            293.097287       365.810819            0.801           0.423
L4.total_qa_bytes_power_log_differenced               -567.105971       362.859621           -1.563           0.118
L4.total_raw_bytes_committed_log_differenced          -193.873350       366.334072           -0.529           0.597
L4.total_raw_bytes_power_log_differenced               467.515605       363.326904            1.287           0.198
L4.burnt_fil_log_differenced                           -58.998466         9.559955           -6.171           0.000
L4.circulating_fil_log_differenced                    -304.670256        48.653066           -6.262           0.000
L4.locked_fil_log_differenced                         2199.802108       748.116852            2.940           0.003
L4.vested_fil_log_differenced                          362.910297       119.519917            3.036           0.002
===================================================================================================================

Results for equation total_qa_bytes_committed_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000013            0.008           0.993
L1.cum_sum_baseline_log_differenced                   9716.040688      3771.967114            2.576           0.010
L1.cum_sum_realized_log_differenced                   -143.748083       458.661926           -0.313           0.754
L1.effective_baseline_power_log_differenced          -5655.426868      1876.147528           -3.014           0.003
L1.effective_network_time_log_differenced            -9475.854144      3981.068010           -2.380           0.017
L1.new_baseline_power_log_differenced                  289.952089      1665.505532            0.174           0.862
L1.total_mined_reward_log_differenced                   88.563668        41.745005            2.122           0.034
L1.miner_count_log_differenced                           0.748832         0.359367            2.084           0.037
L1.participating_miner_count_log_differenced             0.723838         0.088156            8.211           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.612580         0.208537            2.938           0.003
L1.qa_smoothed_velocity_estimate_log_differenced        -0.003719         0.001222           -3.043           0.002
L1.total_pledge_collateral_log_differenced           -6733.619864      1206.003607           -5.583           0.000
L1.total_qa_bytes_committed_log_differenced          -3219.159809       584.147234           -5.511           0.000
L1.total_qa_bytes_power_log_differenced               2676.360650       579.524894            4.618           0.000
L1.total_raw_bytes_committed_log_differenced          3488.380168       585.197971            5.961           0.000
L1.total_raw_bytes_power_log_differenced             -2945.585710       580.481045           -5.074           0.000
L1.burnt_fil_log_differenced                           -24.638700        15.248807           -1.616           0.106
L1.circulating_fil_log_differenced                    -121.182126        77.614401           -1.561           0.118
L1.locked_fil_log_differenced                         6662.378464      1190.886029            5.594           0.000
L1.vested_fil_log_differenced                          148.803507       191.475210            0.777           0.437
L2.cum_sum_baseline_log_differenced                  25773.875440      3980.852441            6.474           0.000
L2.cum_sum_realized_log_differenced                     22.926214       492.338190            0.047           0.963
L2.effective_baseline_power_log_differenced         -14441.998824      1969.094349           -7.334           0.000
L2.effective_network_time_log_differenced           -25489.009464      4211.010125           -6.053           0.000
L2.new_baseline_power_log_differenced                 -149.650170      1795.406331           -0.083           0.934
L2.total_mined_reward_log_differenced                  -25.515050        41.699279           -0.612           0.541
L2.miner_count_log_differenced                           0.194370         0.359673            0.540           0.589
L2.participating_miner_count_log_differenced             0.306346         0.088150            3.475           0.001
L2.qa_smoothed_position_estimate_log_differenced         0.972450         0.208168            4.671           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.001013         0.001246            0.813           0.416
L2.total_pledge_collateral_log_differenced           -5514.823216      1209.287596           -4.560           0.000
L2.total_qa_bytes_committed_log_differenced          -2644.053155       585.122926           -4.519           0.000
L2.total_qa_bytes_power_log_differenced               2162.326208       580.247149            3.727           0.000
L2.total_raw_bytes_committed_log_differenced          2543.525047       585.934070            4.341           0.000
L2.total_raw_bytes_power_log_differenced             -2062.638635       580.971000           -3.550           0.000
L2.burnt_fil_log_differenced                            20.788967        15.235956            1.364           0.172
L2.circulating_fil_log_differenced                      89.184121        77.545864            1.150           0.250
L2.locked_fil_log_differenced                         5574.189870      1194.206948            4.668           0.000
L2.vested_fil_log_differenced                         -118.165801       225.648492           -0.524           0.601
L3.cum_sum_baseline_log_differenced                   1613.365189      3977.275214            0.406           0.685
L3.cum_sum_realized_log_differenced                     15.383742       492.197687            0.031           0.975
L3.effective_baseline_power_log_differenced           -848.027090      1970.347850           -0.430           0.667
L3.effective_network_time_log_differenced            -1590.613059      4206.506489           -0.378           0.705
L3.new_baseline_power_log_differenced                   41.819513      1794.687889            0.023           0.981
L3.total_mined_reward_log_differenced                   85.486485        41.668684            2.052           0.040
L3.miner_count_log_differenced                           0.520661         0.359861            1.447           0.148
L3.participating_miner_count_log_differenced            -0.075006         0.088159           -0.851           0.395
L3.qa_smoothed_position_estimate_log_differenced        -0.262986         0.208172           -1.263           0.206
L3.qa_smoothed_velocity_estimate_log_differenced         0.002702         0.001246            2.168           0.030
L3.total_pledge_collateral_log_differenced             364.359048      1209.214532            0.301           0.763
L3.total_qa_bytes_committed_log_differenced            -15.562120       584.785574           -0.027           0.979
L3.total_qa_bytes_power_log_differenced                -95.901321       579.932178           -0.165           0.869
L3.total_raw_bytes_committed_log_differenced          -280.558419       585.554628           -0.479           0.632
L3.total_raw_bytes_power_log_differenced               392.414974       580.613549            0.676           0.499
L3.burnt_fil_log_differenced                           -38.714217        15.227047           -2.542           0.011
L3.circulating_fil_log_differenced                    -199.150697        77.500249           -2.570           0.010
L3.locked_fil_log_differenced                         -481.978273      1194.126353           -0.404           0.686
L3.vested_fil_log_differenced                          126.612126       225.483545            0.562           0.574
L4.cum_sum_baseline_log_differenced                   3678.183870      3761.947878            0.978           0.328
L4.cum_sum_realized_log_differenced                     46.815734       458.618530            0.102           0.919
L4.effective_baseline_power_log_differenced          -1737.690177      1874.853947           -0.927           0.354
L4.effective_network_time_log_differenced            -3735.207422      3970.078256           -0.941           0.347
L4.new_baseline_power_log_differenced                 -308.587404      1664.942006           -0.185           0.853
L4.total_mined_reward_log_differenced                  269.796651        41.696768            6.470           0.000
L4.miner_count_log_differenced                           1.347998         0.359835            3.746           0.000
L4.participating_miner_count_log_differenced             0.260542         0.088105            2.957           0.003
L4.qa_smoothed_position_estimate_log_differenced        -1.047132         0.207932           -5.036           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000816         0.001220            0.669           0.503
L4.total_pledge_collateral_log_differenced           -3617.689332      1208.135244           -2.994           0.003
L4.total_qa_bytes_committed_log_differenced            453.881641       583.348312            0.778           0.437
L4.total_qa_bytes_power_log_differenced               -882.575962       578.642119           -1.525           0.127
L4.total_raw_bytes_committed_log_differenced          -302.728588       584.182728           -0.518           0.604
L4.total_raw_bytes_power_log_differenced               730.832561       579.387281            1.261           0.207
L4.burnt_fil_log_differenced                           -93.571296        15.244994           -6.138           0.000
L4.circulating_fil_log_differenced                    -483.234733        77.585687           -6.228           0.000
L4.locked_fil_log_differenced                         3333.447603      1193.001081            2.794           0.005
L4.vested_fil_log_differenced                          567.341953       190.595079            2.977           0.003
===================================================================================================================

Results for equation total_qa_bytes_power_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000013            0.008           0.993
L1.cum_sum_baseline_log_differenced                   9716.348592      3772.310507            2.576           0.010
L1.cum_sum_realized_log_differenced                   -143.823983       458.703681           -0.314           0.754
L1.effective_baseline_power_log_differenced          -5655.781144      1876.318330           -3.014           0.003
L1.effective_network_time_log_differenced            -9476.082684      3981.430440           -2.380           0.017
L1.new_baseline_power_log_differenced                  290.187160      1665.657157            0.174           0.862
L1.total_mined_reward_log_differenced                   88.570932        41.748805            2.122           0.034
L1.miner_count_log_differenced                           0.748881         0.359400            2.084           0.037
L1.participating_miner_count_log_differenced             0.723864         0.088164            8.210           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.612638         0.208556            2.938           0.003
L1.qa_smoothed_velocity_estimate_log_differenced        -0.003719         0.001222           -3.043           0.002
L1.total_pledge_collateral_log_differenced           -6734.552497      1206.113400           -5.584           0.000
L1.total_qa_bytes_committed_log_differenced          -3219.349770       584.200414           -5.511           0.000
L1.total_qa_bytes_power_log_differenced               2676.487155       579.577653            4.618           0.000
L1.total_raw_bytes_committed_log_differenced          3488.603721       585.251246            5.961           0.000
L1.total_raw_bytes_power_log_differenced             -2945.745804       580.533891           -5.074           0.000
L1.burnt_fil_log_differenced                           -24.640806        15.250195           -1.616           0.106
L1.circulating_fil_log_differenced                    -121.192050        77.621466           -1.561           0.118
L1.locked_fil_log_differenced                         6663.304326      1190.994446            5.595           0.000
L1.vested_fil_log_differenced                          148.833213       191.492642            0.777           0.437
L2.cum_sum_baseline_log_differenced                  25774.645808      3981.214851            6.474           0.000
L2.cum_sum_realized_log_differenced                     22.923541       492.383012            0.047           0.963
L2.effective_baseline_power_log_differenced         -14442.439340      1969.273612           -7.334           0.000
L2.effective_network_time_log_differenced           -25489.767507      4211.393488           -6.053           0.000
L2.new_baseline_power_log_differenced                 -149.661399      1795.569781           -0.083           0.934
L2.total_mined_reward_log_differenced                  -25.540665        41.703075           -0.612           0.540
L2.miner_count_log_differenced                           0.194519         0.359705            0.541           0.589
L2.participating_miner_count_log_differenced             0.306363         0.088158            3.475           0.001
L2.qa_smoothed_position_estimate_log_differenced         0.972537         0.208187            4.671           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.001014         0.001246            0.813           0.416
L2.total_pledge_collateral_log_differenced           -5515.057328      1209.397687           -4.560           0.000
L2.total_qa_bytes_committed_log_differenced          -2644.225312       585.176195           -4.519           0.000
L2.total_qa_bytes_power_log_differenced               2162.444507       580.299974            3.726           0.000
L2.total_raw_bytes_committed_log_differenced          2543.693675       585.987412            4.341           0.000
L2.total_raw_bytes_power_log_differenced             -2062.753479       581.023891           -3.550           0.000
L2.burnt_fil_log_differenced                            20.799194        15.237343            1.365           0.172
L2.circulating_fil_log_differenced                      89.235549        77.552924            1.151           0.250
L2.locked_fil_log_differenced                         5574.454867      1194.315666            4.667           0.000
L2.vested_fil_log_differenced                         -118.213766       225.669034           -0.524           0.600
L3.cum_sum_baseline_log_differenced                   1612.124490      3977.637299            0.405           0.685
L3.cum_sum_realized_log_differenced                     15.369152       492.242496            0.031           0.975
L3.effective_baseline_power_log_differenced           -847.359819      1970.527227           -0.430           0.667
L3.effective_network_time_log_differenced            -1589.371467      4206.889442           -0.378           0.706
L3.new_baseline_power_log_differenced                   41.858195      1794.851274            0.023           0.981
L3.total_mined_reward_log_differenced                   85.479243        41.672477            2.051           0.040
L3.miner_count_log_differenced                           0.520753         0.359894            1.447           0.148
L3.participating_miner_count_log_differenced            -0.074998         0.088167           -0.851           0.395
L3.qa_smoothed_position_estimate_log_differenced        -0.262981         0.208191           -1.263           0.207
L3.qa_smoothed_velocity_estimate_log_differenced         0.002702         0.001246            2.168           0.030
L3.total_pledge_collateral_log_differenced             364.525269      1209.324617            0.301           0.763
L3.total_qa_bytes_committed_log_differenced            -15.408788       584.838812           -0.026           0.979
L3.total_qa_bytes_power_log_differenced                -96.077219       579.984974           -0.166           0.868
L3.total_raw_bytes_committed_log_differenced          -280.716774       585.607936           -0.479           0.632
L3.total_raw_bytes_power_log_differenced               392.595902       580.666407            0.676           0.499
L3.burnt_fil_log_differenced                           -38.712263        15.228434           -2.542           0.011
L3.circulating_fil_log_differenced                    -199.140293        77.507304           -2.569           0.010
L3.locked_fil_log_differenced                         -482.138842      1194.235064           -0.404           0.686
L3.vested_fil_log_differenced                          126.607566       225.504072            0.561           0.574
L4.cum_sum_baseline_log_differenced                   3678.355494      3762.290359            0.978           0.328
L4.cum_sum_realized_log_differenced                     46.798561       458.660282            0.102           0.919
L4.effective_baseline_power_log_differenced          -1737.816326      1875.024631           -0.927           0.354
L4.effective_network_time_log_differenced            -3735.362813      3970.439685           -0.941           0.347
L4.new_baseline_power_log_differenced                 -308.552446      1665.093579           -0.185           0.853
L4.total_mined_reward_log_differenced                  269.808320        41.700564            6.470           0.000
L4.miner_count_log_differenced                           1.348160         0.359868            3.746           0.000
L4.participating_miner_count_log_differenced             0.260576         0.088113            2.957           0.003
L4.qa_smoothed_position_estimate_log_differenced        -1.047203         0.207951           -5.036           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000816         0.001220            0.669           0.504
L4.total_pledge_collateral_log_differenced           -3618.384247      1208.245231           -2.995           0.003
L4.total_qa_bytes_committed_log_differenced            453.995200       583.401419            0.778           0.436
L4.total_qa_bytes_power_log_differenced               -882.737954       578.694798           -1.525           0.127
L4.total_raw_bytes_committed_log_differenced          -302.808303       584.235911           -0.518           0.604
L4.total_raw_bytes_power_log_differenced               730.960648       579.440028            1.261           0.207
L4.burnt_fil_log_differenced                           -93.575230        15.246382           -6.138           0.000
L4.circulating_fil_log_differenced                    -483.255138        77.592751           -6.228           0.000
L4.locked_fil_log_differenced                         3334.129696      1193.109690            2.794           0.005
L4.vested_fil_log_differenced                          567.380423       190.612431            2.977           0.003
===================================================================================================================

Results for equation total_raw_bytes_committed_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000013            0.008           0.993
L1.cum_sum_baseline_log_differenced                   9712.512621      3771.247797            2.575           0.010
L1.cum_sum_realized_log_differenced                   -143.702541       458.574459           -0.313           0.754
L1.effective_baseline_power_log_differenced          -5653.361799      1875.789746           -3.014           0.003
L1.effective_network_time_log_differenced            -9472.405996      3980.308818           -2.380           0.017
L1.new_baseline_power_log_differenced                  289.887581      1665.187920            0.174           0.862
L1.total_mined_reward_log_differenced                   88.558664        41.737044            2.122           0.034
L1.miner_count_log_differenced                           0.748839         0.359299            2.084           0.037
L1.participating_miner_count_log_differenced             0.723645         0.088139            8.210           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.612501         0.208497            2.938           0.003
L1.qa_smoothed_velocity_estimate_log_differenced        -0.003718         0.001222           -3.043           0.002
L1.total_pledge_collateral_log_differenced           -6731.661726      1205.773622           -5.583           0.000
L1.total_qa_bytes_committed_log_differenced          -3217.918734       584.035837           -5.510           0.000
L1.total_qa_bytes_power_log_differenced               2675.239654       579.414378            4.617           0.000
L1.total_raw_bytes_committed_log_differenced          3487.060177       585.086373            5.960           0.000
L1.total_raw_bytes_power_log_differenced             -2944.385859       580.370347           -5.073           0.000
L1.burnt_fil_log_differenced                           -24.637028        15.245899           -1.616           0.106
L1.circulating_fil_log_differenced                    -121.176399        77.599599           -1.562           0.118
L1.locked_fil_log_differenced                         6660.423286      1190.658927            5.594           0.000
L1.vested_fil_log_differenced                          148.739092       191.438696            0.777           0.437
L2.cum_sum_baseline_log_differenced                  25766.607558      3980.093291            6.474           0.000
L2.cum_sum_realized_log_differenced                     22.894392       492.244301            0.047           0.963
L2.effective_baseline_power_log_differenced         -14438.009881      1968.718841           -7.334           0.000
L2.effective_network_time_log_differenced           -25481.789915      4210.207083           -6.052           0.000
L2.new_baseline_power_log_differenced                 -149.479657      1795.063946           -0.083           0.934
L2.total_mined_reward_log_differenced                  -25.514476        41.691327           -0.612           0.541
L2.miner_count_log_differenced                           0.194299         0.359604            0.540           0.589
L2.participating_miner_count_log_differenced             0.306227         0.088133            3.475           0.001
L2.qa_smoothed_position_estimate_log_differenced         0.972181         0.208129            4.671           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.001013         0.001246            0.813           0.416
L2.total_pledge_collateral_log_differenced           -5513.623781      1209.056984           -4.560           0.000
L2.total_qa_bytes_committed_log_differenced          -2643.385119       585.011343           -4.519           0.000
L2.total_qa_bytes_power_log_differenced               2161.763729       580.136496            3.726           0.000
L2.total_raw_bytes_committed_log_differenced          2542.871864       585.822332            4.341           0.000
L2.total_raw_bytes_power_log_differenced             -2062.090733       580.860209           -3.550           0.000
L2.burnt_fil_log_differenced                            20.785810        15.233050            1.365           0.172
L2.circulating_fil_log_differenced                      89.172753        77.531076            1.150           0.250
L2.locked_fil_log_differenced                         5572.981918      1193.979212            4.668           0.000
L2.vested_fil_log_differenced                         -118.176441       225.605460           -0.524           0.600
L3.cum_sum_baseline_log_differenced                   1612.747847      3976.516746            0.406           0.685
L3.cum_sum_realized_log_differenced                     15.558501       492.103825            0.032           0.975
L3.effective_baseline_power_log_differenced           -847.205939      1969.972104           -0.430           0.667
L3.effective_network_time_log_differenced            -1590.187196      4205.704306           -0.378           0.705
L3.new_baseline_power_log_differenced                   41.169912      1794.345641            0.023           0.982
L3.total_mined_reward_log_differenced                   85.455766        41.660738            2.051           0.040
L3.miner_count_log_differenced                           0.520643         0.359793            1.447           0.148
L3.participating_miner_count_log_differenced            -0.074979         0.088142           -0.851           0.395
L3.qa_smoothed_position_estimate_log_differenced        -0.262887         0.208132           -1.263           0.207
L3.qa_smoothed_velocity_estimate_log_differenced         0.002701         0.001246            2.168           0.030
L3.total_pledge_collateral_log_differenced             363.963280      1208.983934            0.301           0.763
L3.total_qa_bytes_committed_log_differenced            -15.331247       584.674055           -0.026           0.979
L3.total_qa_bytes_power_log_differenced                -96.106230       579.821585           -0.166           0.868
L3.total_raw_bytes_committed_log_differenced          -280.740568       585.442962           -0.480           0.632
L3.total_raw_bytes_power_log_differenced               392.571030       580.502826            0.676           0.499
L3.burnt_fil_log_differenced                           -38.702139        15.224143           -2.542           0.011
L3.circulating_fil_log_differenced                    -199.087594        77.485470           -2.569           0.010
L3.locked_fil_log_differenced                         -481.544876      1193.898633           -0.403           0.687
L3.vested_fil_log_differenced                          126.540583       225.440545            0.561           0.575
L4.cum_sum_baseline_log_differenced                   3676.801516      3761.230472            0.978           0.328
L4.cum_sum_realized_log_differenced                     46.974126       458.531071            0.102           0.918
L4.effective_baseline_power_log_differenced          -1736.530758      1874.496412           -0.926           0.354
L4.effective_network_time_log_differenced            -3733.993469      3969.321160           -0.941           0.347
L4.new_baseline_power_log_differenced                 -309.097455      1664.624500           -0.186           0.853
L4.total_mined_reward_log_differenced                  269.738506        41.688817            6.470           0.000
L4.miner_count_log_differenced                           1.347941         0.359767            3.747           0.000
L4.participating_miner_count_log_differenced             0.260469         0.088089            2.957           0.003
L4.qa_smoothed_position_estimate_log_differenced        -1.046785         0.207892           -5.035           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000815         0.001219            0.669           0.504
L4.total_pledge_collateral_log_differenced           -3617.031743      1207.904852           -2.994           0.003
L4.total_qa_bytes_committed_log_differenced            454.001442       583.237067            0.778           0.436
L4.total_qa_bytes_power_log_differenced               -882.606991       578.531772           -1.526           0.127
L4.total_raw_bytes_committed_log_differenced          -302.875677       584.071324           -0.519           0.604
L4.total_raw_bytes_power_log_differenced               730.891028       579.276792            1.262           0.207
L4.burnt_fil_log_differenced                           -93.550090        15.242086           -6.138           0.000
L4.circulating_fil_log_differenced                    -483.125038        77.570892           -6.228           0.000
L4.locked_fil_log_differenced                         3332.854602      1192.773575            2.794           0.005
L4.vested_fil_log_differenced                          567.168862       190.558733            2.976           0.003
===================================================================================================================

Results for equation total_raw_bytes_power_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000013            0.008           0.993
L1.cum_sum_baseline_log_differenced                   9713.102375      3771.579491            2.575           0.010
L1.cum_sum_realized_log_differenced                   -143.768587       458.614792           -0.313           0.754
L1.effective_baseline_power_log_differenced          -5653.848074      1875.954728           -3.014           0.003
L1.effective_network_time_log_differenced            -9472.923428      3980.658900           -2.380           0.017
L1.new_baseline_power_log_differenced                  290.084763      1665.334378            0.174           0.862
L1.total_mined_reward_log_differenced                   88.564915        41.740715            2.122           0.034
L1.miner_count_log_differenced                           0.748902         0.359330            2.084           0.037
L1.participating_miner_count_log_differenced             0.723677         0.088147            8.210           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.612544         0.208516            2.938           0.003
L1.qa_smoothed_velocity_estimate_log_differenced        -0.003718         0.001222           -3.043           0.002
L1.total_pledge_collateral_log_differenced           -6732.653049      1205.879673           -5.583           0.000
L1.total_qa_bytes_committed_log_differenced          -3218.212934       584.087205           -5.510           0.000
L1.total_qa_bytes_power_log_differenced               2675.470528       579.465340            4.617           0.000
L1.total_raw_bytes_committed_log_differenced          3487.385672       585.137834            5.960           0.000
L1.total_raw_bytes_power_log_differenced             -2944.648008       580.421392           -5.073           0.000
L1.burnt_fil_log_differenced                           -24.638782        15.247240           -1.616           0.106
L1.circulating_fil_log_differenced                    -121.184607        77.606425           -1.562           0.118
L1.locked_fil_log_differenced                         6661.408971      1190.763649            5.594           0.000
L1.vested_fil_log_differenced                          148.768252       191.455533            0.777           0.437
L2.cum_sum_baseline_log_differenced                  25767.218886      3980.443353            6.473           0.000
L2.cum_sum_realized_log_differenced                     22.898621       492.287595            0.047           0.963
L2.effective_baseline_power_log_differenced         -14438.343458      1968.891997           -7.333           0.000
L2.effective_network_time_log_differenced           -25482.397335      4210.577385           -6.052           0.000
L2.new_baseline_power_log_differenced                 -149.512133      1795.221828           -0.083           0.934
L2.total_mined_reward_log_differenced                  -25.542005        41.694994           -0.613           0.540
L2.miner_count_log_differenced                           0.194464         0.359636            0.541           0.589
L2.participating_miner_count_log_differenced             0.306242         0.088141            3.474           0.001
L2.qa_smoothed_position_estimate_log_differenced         0.972261         0.208147            4.671           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.001013         0.001246            0.813           0.416
L2.total_pledge_collateral_log_differenced           -5513.783581      1209.163324           -4.560           0.000
L2.total_qa_bytes_committed_log_differenced          -2643.554424       585.062797           -4.518           0.000
L2.total_qa_bytes_power_log_differenced               2161.881646       580.187521            3.726           0.000
L2.total_raw_bytes_committed_log_differenced          2543.036608       585.873857            4.341           0.000
L2.total_raw_bytes_power_log_differenced             -2062.204157       580.911297           -3.550           0.000
L2.burnt_fil_log_differenced                            20.796694        15.234390            1.365           0.172
L2.circulating_fil_log_differenced                      89.227543        77.537895            1.151           0.250
L2.locked_fil_log_differenced                         5573.174641      1194.084226            4.667           0.000
L2.vested_fil_log_differenced                         -118.231830       225.625303           -0.524           0.600
L3.cum_sum_baseline_log_differenced                   1611.194859      3976.866494            0.405           0.685
L3.cum_sum_realized_log_differenced                     15.548895       492.147107            0.032           0.975
L3.effective_baseline_power_log_differenced           -846.351644      1970.145369           -0.430           0.667
L3.effective_network_time_log_differenced            -1588.641633      4206.074212           -0.378           0.706
L3.new_baseline_power_log_differenced                   41.195190      1794.503459            0.023           0.982
L3.total_mined_reward_log_differenced                   85.446138        41.664402            2.051           0.040
L3.miner_count_log_differenced                           0.520763         0.359824            1.447           0.148
L3.participating_miner_count_log_differenced            -0.074980         0.088150           -0.851           0.395
L3.qa_smoothed_position_estimate_log_differenced        -0.262889         0.208150           -1.263           0.207
L3.qa_smoothed_velocity_estimate_log_differenced         0.002701         0.001246            2.168           0.030
L3.total_pledge_collateral_log_differenced             364.197200      1209.090268            0.301           0.763
L3.total_qa_bytes_committed_log_differenced            -15.237028       584.725479           -0.026           0.979
L3.total_qa_bytes_power_log_differenced                -96.221974       579.872582           -0.166           0.868
L3.total_raw_bytes_committed_log_differenced          -280.838376       585.494454           -0.480           0.631
L3.total_raw_bytes_power_log_differenced               392.690380       580.553883            0.676           0.499
L3.burnt_fil_log_differenced                           -38.699380        15.225482           -2.542           0.011
L3.circulating_fil_log_differenced                    -199.072826        77.492285           -2.569           0.010
L3.locked_fil_log_differenced                         -481.770522      1194.003640           -0.403           0.687
L3.vested_fil_log_differenced                          126.527890       225.460373            0.561           0.575
L4.cum_sum_baseline_log_differenced                   3677.031133      3761.561285            0.978           0.328
L4.cum_sum_realized_log_differenced                     46.960714       458.571401            0.102           0.918
L4.effective_baseline_power_log_differenced          -1736.681531      1874.661280           -0.926           0.354
L4.effective_network_time_log_differenced            -3734.209275      3969.670275           -0.941           0.347
L4.new_baseline_power_log_differenced                 -309.074774      1664.770910           -0.186           0.853
L4.total_mined_reward_log_differenced                  269.745510        41.692483            6.470           0.000
L4.miner_count_log_differenced                           1.348102         0.359799            3.747           0.000
L4.participating_miner_count_log_differenced             0.260501         0.088096            2.957           0.003
L4.qa_smoothed_position_estimate_log_differenced        -1.046858         0.207910           -5.035           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000815         0.001219            0.669           0.504
L4.total_pledge_collateral_log_differenced           -3617.676211      1208.011092           -2.995           0.003
L4.total_qa_bytes_committed_log_differenced            454.064345       583.288365            0.778           0.436
L4.total_qa_bytes_power_log_differenced               -882.715515       578.582656           -1.526           0.127
L4.total_raw_bytes_committed_log_differenced          -302.907517       584.122695           -0.519           0.604
L4.total_raw_bytes_power_log_differenced               730.968442       579.327741            1.262           0.207
L4.burnt_fil_log_differenced                           -93.552372        15.243427           -6.137           0.000
L4.circulating_fil_log_differenced                    -483.137071        77.577714           -6.228           0.000
L4.locked_fil_log_differenced                         3333.491328      1192.878484            2.794           0.005
L4.vested_fil_log_differenced                          567.196741       190.575493            2.976           0.003
===================================================================================================================

Results for equation burnt_fil_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000003            0.004           0.997
L1.cum_sum_baseline_log_differenced                   1749.490625       746.789188            2.343           0.019
L1.cum_sum_realized_log_differenced                    -39.353279        90.807729           -0.433           0.665
L1.effective_baseline_power_log_differenced          -1053.990858       371.447218           -2.838           0.005
L1.effective_network_time_log_differenced            -1691.854699       788.187823           -2.147           0.032
L1.new_baseline_power_log_differenced                  108.809550       329.743470            0.330           0.741
L1.total_mined_reward_log_differenced                   23.429507         8.264844            2.835           0.005
L1.miner_count_log_differenced                           0.108121         0.071149            1.520           0.129
L1.participating_miner_count_log_differenced             0.127758         0.017453            7.320           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.171643         0.041287            4.157           0.000
L1.qa_smoothed_velocity_estimate_log_differenced        -0.000810         0.000242           -3.347           0.001
L1.total_pledge_collateral_log_differenced           -1331.072180       238.769435           -5.575           0.000
L1.total_qa_bytes_committed_log_differenced           -520.241860       115.651814           -4.498           0.000
L1.total_qa_bytes_power_log_differenced                413.377199       114.736664            3.603           0.000
L1.total_raw_bytes_committed_log_differenced           578.876118       115.859843            4.996           0.000
L1.total_raw_bytes_power_log_differenced              -472.070843       114.925967           -4.108           0.000
L1.burnt_fil_log_differenced                            -6.870286         3.019020           -2.276           0.023
L1.circulating_fil_log_differenced                     -34.338738        15.366411           -2.235           0.025
L1.locked_fil_log_differenced                         1310.554722       235.776396            5.558           0.000
L1.vested_fil_log_differenced                           33.035694        37.909031            0.871           0.384
L2.cum_sum_baseline_log_differenced                   5235.259537       788.145144            6.643           0.000
L2.cum_sum_realized_log_differenced                     -5.910183        97.475091           -0.061           0.952
L2.effective_baseline_power_log_differenced          -2963.199126       389.849202           -7.601           0.000
L2.effective_network_time_log_differenced            -5166.870074       833.712686           -6.197           0.000
L2.new_baseline_power_log_differenced                    5.604732       355.461751            0.016           0.987
L2.total_mined_reward_log_differenced                   -3.224957         8.255791           -0.391           0.696
L2.miner_count_log_differenced                           0.028103         0.071209            0.395           0.693
L2.participating_miner_count_log_differenced             0.061632         0.017452            3.531           0.000
L2.qa_smoothed_position_estimate_log_differenced         0.184223         0.041214            4.470           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.000293         0.000247            1.188           0.235
L2.total_pledge_collateral_log_differenced           -1279.515890       239.419612           -5.344           0.000
L2.total_qa_bytes_committed_log_differenced           -571.256594       115.844985           -4.931           0.000
L2.total_qa_bytes_power_log_differenced                471.337839       114.879660            4.103           0.000
L2.total_raw_bytes_committed_log_differenced           557.999689       116.005579            4.810           0.000
L2.total_raw_bytes_power_log_differenced              -458.238767       115.022970           -3.984           0.000
L2.burnt_fil_log_differenced                             3.143356         3.016476            1.042           0.297
L2.circulating_fil_log_differenced                      13.118427        15.352841            0.854           0.393
L2.locked_fil_log_differenced                         1288.505573       236.433885            5.450           0.000
L2.vested_fil_log_differenced                          -12.123051        44.674794           -0.271           0.786
L3.cum_sum_baseline_log_differenced                    403.087860       787.436910            0.512           0.609
L3.cum_sum_realized_log_differenced                      9.457461        97.447274            0.097           0.923
L3.effective_baseline_power_log_differenced           -191.846871       390.097376           -0.492           0.623
L3.effective_network_time_log_differenced             -406.163563       832.821038           -0.488           0.626
L3.new_baseline_power_log_differenced                  -22.571378       355.319511           -0.064           0.949
L3.total_mined_reward_log_differenced                   25.171756         8.249733            3.051           0.002
L3.miner_count_log_differenced                           0.082016         0.071247            1.151           0.250
L3.participating_miner_count_log_differenced            -0.008129         0.017454           -0.466           0.641
L3.qa_smoothed_position_estimate_log_differenced        -0.016108         0.041215           -0.391           0.696
L3.qa_smoothed_velocity_estimate_log_differenced         0.000672         0.000247            2.722           0.006
L3.total_pledge_collateral_log_differenced            -108.015556       239.405146           -0.451           0.652
L3.total_qa_bytes_committed_log_differenced            135.941376       115.778195            1.174           0.240
L3.total_qa_bytes_power_log_differenced               -160.567034       114.817300           -1.398           0.162
L3.total_raw_bytes_committed_log_differenced          -194.868538       115.930455           -1.681           0.093
L3.total_raw_bytes_power_log_differenced               219.533262       114.952201            1.910           0.056
L3.burnt_fil_log_differenced                           -10.720266         3.014712           -3.556           0.000
L3.circulating_fil_log_differenced                     -54.854125        15.343810           -3.575           0.000
L3.locked_fil_log_differenced                           75.374679       236.417928            0.319           0.750
L3.vested_fil_log_differenced                           47.712668        44.642137            1.069           0.285
L4.cum_sum_baseline_log_differenced                    540.677628       744.805540            0.726           0.468
L4.cum_sum_realized_log_differenced                      4.359393        90.799137            0.048           0.962
L4.effective_baseline_power_log_differenced           -251.735405       371.191109           -0.678           0.498
L4.effective_network_time_log_differenced             -549.517965       786.012027           -0.699           0.484
L4.new_baseline_power_log_differenced                  -35.621386       329.631901           -0.108           0.914
L4.total_mined_reward_log_differenced                   63.436447         8.255294            7.684           0.000
L4.miner_count_log_differenced                           0.239736         0.071242            3.365           0.001
L4.participating_miner_count_log_differenced             0.049827         0.017443            2.857           0.004
L4.qa_smoothed_position_estimate_log_differenced        -0.204135         0.041167           -4.959           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000209         0.000241            0.867           0.386
L4.total_pledge_collateral_log_differenced            -839.203150       239.191465           -3.508           0.000
L4.total_qa_bytes_committed_log_differenced            139.803338       115.493640            1.210           0.226
L4.total_qa_bytes_power_log_differenced               -227.783446       114.561889           -1.988           0.047
L4.total_raw_bytes_committed_log_differenced           -99.117007       115.658841           -0.857           0.391
L4.total_raw_bytes_power_log_differenced               186.945551       114.709419            1.630           0.103
L4.burnt_fil_log_differenced                           -22.155180         3.018265           -7.340           0.000
L4.circulating_fil_log_differenced                    -113.878688        15.360726           -7.414           0.000
L4.locked_fil_log_differenced                          771.880797       236.195142            3.268           0.001
L4.vested_fil_log_differenced                          128.327281        37.734779            3.401           0.001
===================================================================================================================

Results for equation circulating_fil_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000008            0.010           0.992
L1.cum_sum_baseline_log_differenced                   6930.765972      2179.989968            3.179           0.001
L1.cum_sum_realized_log_differenced                    -41.495464       265.081420           -0.157           0.876
L1.effective_baseline_power_log_differenced          -3891.452717      1084.310300           -3.589           0.000
L1.effective_network_time_log_differenced            -6822.332598      2300.838810           -2.965           0.003
L1.new_baseline_power_log_differenced                   -6.345853       962.570787           -0.007           0.995
L1.total_mined_reward_log_differenced                   51.670519        24.126322            2.142           0.032
L1.miner_count_log_differenced                           0.392184         0.207694            1.888           0.059
L1.participating_miner_count_log_differenced             0.429153         0.050949            8.423           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.257678         0.120523            2.138           0.033
L1.qa_smoothed_velocity_estimate_log_differenced        -0.001983         0.000706           -2.807           0.005
L1.total_pledge_collateral_log_differenced           -4209.322372       697.003894           -6.039           0.000
L1.total_qa_bytes_committed_log_differenced          -2017.772160       337.605041           -5.977           0.000
L1.total_qa_bytes_power_log_differenced               1706.824247       334.933582            5.096           0.000
L1.total_raw_bytes_committed_log_differenced          2170.517080       338.212309            6.418           0.000
L1.total_raw_bytes_power_log_differenced             -1859.464561       335.486184           -5.543           0.000
L1.burnt_fil_log_differenced                           -14.374731         8.812973           -1.631           0.103
L1.circulating_fil_log_differenced                     -70.936795        44.856864           -1.581           0.114
L1.locked_fil_log_differenced                         4167.596419       688.266764            6.055           0.000
L1.vested_fil_log_differenced                          104.388810       110.662162            0.943           0.346
L2.cum_sum_baseline_log_differenced                  15754.343615      2300.714223            6.848           0.000
L2.cum_sum_realized_log_differenced                     40.815939       284.544452            0.143           0.886
L2.effective_baseline_power_log_differenced          -8755.555673      1138.028460           -7.694           0.000
L2.effective_network_time_log_differenced           -15608.997858      2433.732732           -6.414           0.000
L2.new_baseline_power_log_differenced                 -194.361548      1037.646319           -0.187           0.851
L2.total_mined_reward_log_differenced                  -16.703414        24.099895           -0.693           0.488
L2.miner_count_log_differenced                           0.084875         0.207871            0.408           0.683
L2.participating_miner_count_log_differenced             0.181126         0.050946            3.555           0.000
L2.qa_smoothed_position_estimate_log_differenced         0.549002         0.120310            4.563           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.000609         0.000720            0.845           0.398
L2.total_pledge_collateral_log_differenced           -3200.799530       698.901859           -4.580           0.000
L2.total_qa_bytes_committed_log_differenced          -1562.153626       338.168937           -4.619           0.000
L2.total_qa_bytes_power_log_differenced               1288.957203       335.351006            3.844           0.000
L2.total_raw_bytes_committed_log_differenced          1502.271977       338.637734            4.436           0.000
L2.total_raw_bytes_power_log_differenced             -1229.548068       335.769352           -3.662           0.000
L2.burnt_fil_log_differenced                            12.982430         8.805546            1.474           0.140
L2.circulating_fil_log_differenced                      55.802428        44.817253            1.245           0.213
L2.locked_fil_log_differenced                         3237.699616       690.186072            4.691           0.000
L2.vested_fil_log_differenced                          -67.305994       130.412444           -0.516           0.606
L3.cum_sum_baseline_log_differenced                   1510.101404      2298.646782            0.657           0.511
L3.cum_sum_realized_log_differenced                     -3.122553       284.463249           -0.011           0.991
L3.effective_baseline_power_log_differenced           -852.383472      1138.752915           -0.749           0.454
L3.effective_network_time_log_differenced            -1477.429294      2431.129878           -0.608           0.543
L3.new_baseline_power_log_differenced                   62.699610      1037.231099            0.060           0.952
L3.total_mined_reward_log_differenced                   45.452076        24.082212            1.887           0.059
L3.miner_count_log_differenced                           0.283901         0.207980            1.365           0.172
L3.participating_miner_count_log_differenced            -0.050437         0.050951           -0.990           0.322
L3.qa_smoothed_position_estimate_log_differenced        -0.214236         0.120312           -1.781           0.075
L3.qa_smoothed_velocity_estimate_log_differenced         0.001537         0.000720            2.134           0.033
L3.total_pledge_collateral_log_differenced             200.895454       698.859632            0.287           0.774
L3.total_qa_bytes_committed_log_differenced           -177.089988       337.973966           -0.524           0.600
L3.total_qa_bytes_power_log_differenced                115.165246       335.168969            0.344           0.731
L3.total_raw_bytes_committed_log_differenced             2.832643       338.418437            0.008           0.993
L3.total_raw_bytes_power_log_differenced                59.394495       335.562764            0.177           0.860
L3.burnt_fil_log_differenced                           -21.338892         8.800398           -2.425           0.015
L3.circulating_fil_log_differenced                    -110.193708        44.790890           -2.460           0.014
L3.locked_fil_log_differenced                         -265.785291       690.139493           -0.385           0.700
L3.vested_fil_log_differenced                           78.379701       130.317113            0.601           0.548
L4.cum_sum_baseline_log_differenced                   2714.854755      2174.199400            1.249           0.212
L4.cum_sum_realized_log_differenced                     35.048375       265.056339            0.132           0.895
L4.effective_baseline_power_log_differenced          -1312.134024      1083.562681           -1.211           0.226
L4.effective_network_time_log_differenced            -2750.822117      2294.487335           -1.199           0.231
L4.new_baseline_power_log_differenced                 -223.165676       962.245099           -0.232           0.817
L4.total_mined_reward_log_differenced                  152.916202        24.098444            6.345           0.000
L4.miner_count_log_differenced                           0.799158         0.207965            3.843           0.000
L4.participating_miner_count_log_differenced             0.159176         0.050920            3.126           0.002
L4.qa_smoothed_position_estimate_log_differenced        -0.582491         0.120173           -4.847           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000450         0.000705            0.638           0.523
L4.total_pledge_collateral_log_differenced           -2073.100163       698.235863           -2.969           0.003
L4.total_qa_bytes_committed_log_differenced            230.636815       337.143308            0.684           0.494
L4.total_qa_bytes_power_log_differenced               -474.143440       334.423386           -1.418           0.156
L4.total_raw_bytes_committed_log_differenced          -145.432222       337.625554           -0.431           0.667
L4.total_raw_bytes_power_log_differenced               388.628885       334.854049            1.161           0.246
L4.burnt_fil_log_differenced                           -53.083696         8.810770           -6.025           0.000
L4.circulating_fil_log_differenced                    -274.637574        44.840269           -6.125           0.000
L4.locked_fil_log_differenced                         1911.739999       689.489147            2.773           0.006
L4.vested_fil_log_differenced                          337.184716       110.153495            3.061           0.002
===================================================================================================================

Results for equation locked_fil_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000008            0.009           0.993
L1.cum_sum_baseline_log_differenced                   6782.672324      2365.658363            2.867           0.004
L1.cum_sum_realized_log_differenced                    -73.225294       287.658240           -0.255           0.799
L1.effective_baseline_power_log_differenced          -3885.180202      1176.660336           -3.302           0.001
L1.effective_network_time_log_differenced            -6643.218389      2496.799826           -2.661           0.008
L1.new_baseline_power_log_differenced                  110.535503      1044.552345            0.106           0.916
L1.total_mined_reward_log_differenced                   61.092508        26.181146            2.333           0.020
L1.miner_count_log_differenced                           0.436980         0.225384            1.939           0.053
L1.participating_miner_count_log_differenced             0.446283         0.055288            8.072           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.334998         0.130788            2.561           0.010
L1.qa_smoothed_velocity_estimate_log_differenced        -0.002329         0.000766           -3.039           0.002
L1.total_pledge_collateral_log_differenced           -4566.528142       756.367284           -6.037           0.000
L1.total_qa_bytes_committed_log_differenced          -2047.847647       366.358653           -5.590           0.000
L1.total_qa_bytes_power_log_differenced               1693.197610       363.459667            4.659           0.000
L1.total_raw_bytes_committed_log_differenced          2212.874279       367.017642            6.029           0.000
L1.total_raw_bytes_power_log_differenced             -1858.167844       364.059335           -5.104           0.000
L1.burnt_fil_log_differenced                           -17.161480         9.563569           -1.794           0.073
L1.circulating_fil_log_differenced                     -85.018234        48.677295           -1.747           0.081
L1.locked_fil_log_differenced                         4516.108220       746.886017            6.047           0.000
L1.vested_fil_log_differenced                          110.059580       120.087190            0.916           0.359
L2.cum_sum_baseline_log_differenced                  16340.252863      2496.664628            6.545           0.000
L2.cum_sum_realized_log_differenced                     28.850970       308.778927            0.093           0.926
L2.effective_baseline_power_log_differenced          -9115.295310      1234.953639           -7.381           0.000
L2.effective_network_time_log_differenced           -16176.165650      2641.012241           -6.125           0.000
L2.new_baseline_power_log_differenced                 -157.750294      1126.022013           -0.140           0.889
L2.total_mined_reward_log_differenced                  -18.157616        26.152468           -0.694           0.487
L2.miner_count_log_differenced                           0.136647         0.225575            0.606           0.545
L2.participating_miner_count_log_differenced             0.192540         0.055285            3.483           0.000
L2.qa_smoothed_position_estimate_log_differenced         0.577008         0.130557            4.420           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.000654         0.000782            0.836           0.403
L2.total_pledge_collateral_log_differenced           -3566.460668       758.426897           -4.702           0.000
L2.total_qa_bytes_committed_log_differenced          -1678.854190       366.970576           -4.575           0.000
L2.total_qa_bytes_power_log_differenced               1367.499292       363.912643            3.758           0.000
L2.total_raw_bytes_committed_log_differenced          1616.336590       367.479300            4.398           0.000
L2.total_raw_bytes_power_log_differenced             -1305.466965       364.366619           -3.583           0.000
L2.burnt_fil_log_differenced                            13.945662         9.555509            1.459           0.144
L2.circulating_fil_log_differenced                      60.656168        48.634311            1.247           0.212
L2.locked_fil_log_differenced                         3606.378010       748.968792            4.815           0.000
L2.vested_fil_log_differenced                          -70.087774       141.519591           -0.495           0.620
L3.cum_sum_baseline_log_differenced                   1429.420115      2494.421105            0.573           0.567
L3.cum_sum_realized_log_differenced                     14.485362       308.690808            0.047           0.963
L3.effective_baseline_power_log_differenced           -752.160060      1235.739796           -0.609           0.543
L3.effective_network_time_log_differenced            -1416.593591      2638.187703           -0.537           0.591
L3.new_baseline_power_log_differenced                   -3.859464      1125.571429           -0.003           0.997
L3.total_mined_reward_log_differenced                   51.712762        26.133279            1.979           0.048
L3.miner_count_log_differenced                           0.303958         0.225694            1.347           0.178
L3.participating_miner_count_log_differenced            -0.040957         0.055290           -0.741           0.459
L3.qa_smoothed_position_estimate_log_differenced        -0.188917         0.130559           -1.447           0.148
L3.qa_smoothed_velocity_estimate_log_differenced         0.001724         0.000782            2.206           0.027
L3.total_pledge_collateral_log_differenced              88.945131       758.381074            0.117           0.907
L3.total_qa_bytes_committed_log_differenced            -37.374161       366.758999           -0.102           0.919
L3.total_qa_bytes_power_log_differenced                -37.512633       363.715103           -0.103           0.918
L3.total_raw_bytes_committed_log_differenced          -148.576936       367.241326           -0.405           0.686
L3.total_raw_bytes_power_log_differenced               223.742975       364.142437            0.614           0.539
L3.burnt_fil_log_differenced                           -23.650988         9.549922           -2.477           0.013
L3.circulating_fil_log_differenced                    -121.821356        48.605703           -2.506           0.012
L3.locked_fil_log_differenced                         -160.909213       748.918246           -0.215           0.830
L3.vested_fil_log_differenced                           87.605539       141.416141            0.619           0.536
L4.cum_sum_baseline_log_differenced                   2509.828594      2359.374616            1.064           0.287
L4.cum_sum_realized_log_differenced                     51.600504       287.631023            0.179           0.858
L4.effective_baseline_power_log_differenced          -1142.603169      1175.849043           -0.972           0.331
L4.effective_network_time_log_differenced            -2567.901273      2489.907400           -1.031           0.302
L4.new_baseline_power_log_differenced                 -280.466460      1044.198918           -0.269           0.788
L4.total_mined_reward_log_differenced                  170.574877        26.150893            6.523           0.000
L4.miner_count_log_differenced                           0.858229         0.225677            3.803           0.000
L4.participating_miner_count_log_differenced             0.169116         0.055257            3.061           0.002
L4.qa_smoothed_position_estimate_log_differenced        -0.626333         0.130408           -4.803           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000497         0.000765            0.650           0.516
L4.total_pledge_collateral_log_differenced           -2379.454772       757.704179           -3.140           0.002
L4.total_qa_bytes_committed_log_differenced            293.145214       365.857594            0.801           0.423
L4.total_qa_bytes_power_log_differenced               -567.188017       362.906019           -1.563           0.118
L4.total_raw_bytes_committed_log_differenced          -193.906223       366.380913           -0.529           0.597
L4.total_raw_bytes_power_log_differenced               467.582536       363.373361            1.287           0.198
L4.burnt_fil_log_differenced                           -59.007432         9.561177           -6.172           0.000
L4.circulating_fil_log_differenced                    -304.716490        48.659287           -6.262           0.000
L4.locked_fil_log_differenced                         2200.074708       748.212511            2.940           0.003
L4.vested_fil_log_differenced                          362.965916       119.535200            3.036           0.002
===================================================================================================================

Results for equation vested_fil_log_differenced
===================================================================================================================
                                                      coefficient       std. error           t-stat            prob
-------------------------------------------------------------------------------------------------------------------
const                                                    0.000000         0.000006            0.009           0.993
L1.cum_sum_baseline_log_differenced                   5196.016967      1707.577810            3.043           0.002
L1.cum_sum_realized_log_differenced                    -41.506640       207.637263           -0.200           0.842
L1.effective_baseline_power_log_differenced          -2942.323935       849.336113           -3.464           0.001
L1.effective_network_time_log_differenced            -5103.988287      1802.238246           -2.832           0.005
L1.new_baseline_power_log_differenced                   33.351071       753.978018            0.044           0.965
L1.total_mined_reward_log_differenced                   42.162301        18.898056            2.231           0.026
L1.miner_count_log_differenced                           0.307905         0.162686            1.893           0.058
L1.participating_miner_count_log_differenced             0.330312         0.039908            8.277           0.000
L1.qa_smoothed_position_estimate_log_differenced         0.223448         0.094405            2.367           0.018
L1.qa_smoothed_velocity_estimate_log_differenced        -0.001608         0.000553           -2.907           0.004
L1.total_pledge_collateral_log_differenced           -3285.424561       545.960486           -6.018           0.000
L1.total_qa_bytes_committed_log_differenced          -1532.060527       264.444738           -5.793           0.000
L1.total_qa_bytes_power_log_differenced               1284.422528       262.352194            4.896           0.000
L1.total_raw_bytes_committed_log_differenced          1652.387898       264.920409            6.237           0.000
L1.total_raw_bytes_power_log_differenced             -1404.690971       262.785046           -5.345           0.000
L1.burnt_fil_log_differenced                           -11.793079         6.903168           -1.708           0.088
L1.circulating_fil_log_differenced                     -58.309835        35.136210           -1.660           0.097
L1.locked_fil_log_differenced                         3251.002220       539.116725            6.030           0.000
L1.vested_fil_log_differenced                           80.375504        86.681249            0.927           0.354
L2.cum_sum_baseline_log_differenced                  12163.386514      1802.140657            6.749           0.000
L2.cum_sum_realized_log_differenced                     26.526261       222.882582            0.119           0.905
L2.effective_baseline_power_log_differenced          -6772.995008       891.413343           -7.598           0.000
L2.effective_network_time_log_differenced           -12046.121201      1906.333547           -6.319           0.000
L2.new_baseline_power_log_differenced                 -132.917958       812.784395           -0.164           0.870
L2.total_mined_reward_log_differenced                  -12.872734        18.877355           -0.682           0.495
L2.miner_count_log_differenced                           0.077208         0.162825            0.474           0.635
L2.participating_miner_count_log_differenced             0.141061         0.039906            3.535           0.000
L2.qa_smoothed_position_estimate_log_differenced         0.425730         0.094238            4.518           0.000
L2.qa_smoothed_velocity_estimate_log_differenced         0.000483         0.000564            0.856           0.392
L2.total_pledge_collateral_log_differenced           -2547.486060       547.447155           -4.653           0.000
L2.total_qa_bytes_committed_log_differenced          -1224.633778       264.886436           -4.623           0.000
L2.total_qa_bytes_power_log_differenced               1006.440610       262.679161            3.831           0.000
L2.total_raw_bytes_committed_log_differenced          1178.901891       265.253642            4.444           0.000
L2.total_raw_bytes_power_log_differenced              -961.072469       263.006850           -3.654           0.000
L2.burnt_fil_log_differenced                            10.028774         6.897351            1.454           0.146
L2.circulating_fil_log_differenced                      43.234741        35.105183            1.232           0.218
L2.locked_fil_log_differenced                         2576.059474       540.620112            4.765           0.000
L2.vested_fil_log_differenced                          -51.312223       102.151569           -0.502           0.615
L3.cum_sum_baseline_log_differenced                   1124.290892      1800.521239            0.624           0.532
L3.cum_sum_realized_log_differenced                      2.797091       222.818976            0.013           0.990
L3.effective_baseline_power_log_differenced           -618.338168       891.980806           -0.693           0.488
L3.effective_network_time_log_differenced            -1105.355133      1904.294741           -0.580           0.562
L3.new_baseline_power_log_differenced                   28.101496       812.459155            0.035           0.972
L3.total_mined_reward_log_differenced                   37.039960        18.863505            1.964           0.050
L3.miner_count_log_differenced                           0.220166         0.162910            1.351           0.177
L3.participating_miner_count_log_differenced            -0.035453         0.039910           -0.888           0.374
L3.qa_smoothed_position_estimate_log_differenced        -0.152356         0.094240           -1.617           0.106
L3.qa_smoothed_velocity_estimate_log_differenced         0.001233         0.000564            2.186           0.029
L3.total_pledge_collateral_log_differenced             112.421562       547.414079            0.205           0.837
L3.total_qa_bytes_committed_log_differenced            -84.577853       264.733716           -0.319           0.749
L3.total_qa_bytes_power_log_differenced                 33.988664       262.536573            0.129           0.897
L3.total_raw_bytes_committed_log_differenced           -51.277893       265.081868           -0.193           0.847
L3.total_raw_bytes_power_log_differenced               102.086545       262.845031            0.388           0.698
L3.burnt_fil_log_differenced                           -17.143664         6.893318           -2.487           0.013
L3.circulating_fil_log_differenced                     -88.411097        35.084533           -2.520           0.012
L3.locked_fil_log_differenced                         -164.568071       540.583627           -0.304           0.761
L3.vested_fil_log_differenced                           63.719333       102.076897            0.624           0.532
L4.cum_sum_baseline_log_differenced                   1990.093314      1703.042080            1.169           0.243
L4.cum_sum_realized_log_differenced                     29.697324       207.617617            0.143           0.886
L4.effective_baseline_power_log_differenced           -945.103260       848.750506           -1.114           0.265
L4.effective_network_time_log_differenced            -2022.172696      1797.263160           -1.125           0.261
L4.new_baseline_power_log_differenced                 -179.222375       753.722909           -0.238           0.812
L4.total_mined_reward_log_differenced                  122.063635        18.876219            6.467           0.000
L4.miner_count_log_differenced                           0.621217         0.162898            3.814           0.000
L4.participating_miner_count_log_differenced             0.123567         0.039886            3.098           0.002
L4.qa_smoothed_position_estimate_log_differenced        -0.455566         0.094131           -4.840           0.000
L4.qa_smoothed_velocity_estimate_log_differenced         0.000360         0.000552            0.652           0.515
L4.total_pledge_collateral_log_differenced           -1667.909896       546.925483           -3.050           0.002
L4.total_qa_bytes_committed_log_differenced            196.817879       264.083064            0.745           0.456
L4.total_qa_bytes_power_log_differenced               -390.453083       261.952560           -1.491           0.136
L4.total_raw_bytes_committed_log_differenced          -127.352049       264.460806           -0.482           0.630
L4.total_raw_bytes_power_log_differenced               320.732548       262.289897            1.223           0.221
L4.burnt_fil_log_differenced                           -42.335732         6.901442           -6.134           0.000
L4.circulating_fil_log_differenced                    -218.828513        35.123211           -6.230           0.000
L4.locked_fil_log_differenced                         1539.217652       540.074214            2.850           0.004
L4.vested_fil_log_differenced                          264.950650        86.282812            3.071           0.002
===================================================================================================================

Correlation matrix of residuals
                                                 cum_sum_baseline_log_differenced  cum_sum_realized_log_differenced  effective_baseline_power_log_differenced  effective_network_time_log_differenced  new_baseline_power_log_differenced  total_mined_reward_log_differenced  miner_count_log_differenced  participating_miner_count_log_differenced  qa_smoothed_position_estimate_log_differenced  qa_smoothed_velocity_estimate_log_differenced  total_pledge_collateral_log_differenced  total_qa_bytes_committed_log_differenced  total_qa_bytes_power_log_differenced  total_raw_bytes_committed_log_differenced  total_raw_bytes_power_log_differenced  burnt_fil_log_differenced  circulating_fil_log_differenced  locked_fil_log_differenced  vested_fil_log_differenced
cum_sum_baseline_log_differenced                                         1.000000                          1.000000                                  0.999887                                0.999994                            0.999869                            0.999999                     0.883384                                   0.993365                                       0.999132                                      -0.701787                                 0.999641                                  0.999022                              0.999022                                   0.999021                               0.999021                   0.984772                         0.999404                    0.999641                    0.999965
cum_sum_realized_log_differenced                                         1.000000                          1.000000                                  0.999887                                0.999994                            0.999869                            0.999999                     0.883384                                   0.993365                                       0.999132                                      -0.701787                                 0.999641                                  0.999022                              0.999022                                   0.999021                               0.999021                   0.984772                         0.999404                    0.999641                    0.999965
effective_baseline_power_log_differenced                                 0.999887                          0.999887                                  1.000000                                0.999829                            0.999999                            0.999864                     0.888478                                   0.992439                                       0.998705                                      -0.703956                                 0.999138                                  0.998602                              0.998602                                   0.998599                               0.998599                   0.983129                         0.999780                    0.999138                    0.999977
effective_network_time_log_differenced                                   0.999994                          0.999994                                  0.999829                                1.000000                            0.999807                            0.999998                     0.882186                                   0.993546                                       0.999198                                      -0.701266                                 0.999724                                  0.999087                              0.999087                                   0.999086                               0.999086                   0.985118                         0.999285                    0.999724                    0.999930
new_baseline_power_log_differenced                                       0.999869                          0.999869                                  0.999999                                0.999807                            1.000000                            0.999846                     0.888849                                   0.992362                                       0.998665                                      -0.704113                                 0.999092                                  0.998562                              0.998562                                   0.998559                               0.998559                   0.982996                         0.999799                    0.999092                    0.999969
total_mined_reward_log_differenced                                       0.999999                          0.999999                                  0.999864                                0.999998                            0.999846                            1.000000                     0.882805                                   0.993430                                       0.999163                                      -0.701640                                 0.999678                                  0.999058                              0.999058                                   0.999056                               0.999056                   0.984918                         0.999356                    0.999678                    0.999952
miner_count_log_differenced                                              0.883384                          0.883384                                  0.888478                                0.882186                            0.888849                            0.882805                     1.000000                                   0.854856                                       0.874587                                      -0.687846                                 0.872436                                  0.871857                              0.871852                                   0.871825                               0.871822                   0.813834                         0.896486                    0.872433                    0.886212
participating_miner_count_log_differenced                                0.993365                          0.993365                                  0.992439                                0.993546                            0.992362                            0.993430                     0.854856                                   1.000000                                       0.993992                                      -0.693222                                 0.994398                                  0.994024                              0.994027                                   0.994027                               0.994029                   0.986321                         0.990845                    0.994398                    0.992881
qa_smoothed_position_estimate_log_differenced                            0.999132                          0.999132                                  0.998705                                0.999198                            0.998665                            0.999163                     0.874587                                   0.993992                                       1.000000                                      -0.690486                                 0.999327                                  0.999799                              0.999799                                   0.999799                               0.999799                   0.986356                         0.997831                    0.999327                    0.998924
qa_smoothed_velocity_estimate_log_differenced                           -0.701787                         -0.701787                                 -0.703956                               -0.701266                           -0.704113                           -0.701640                    -0.687846                                  -0.693222                                      -0.690486                                       1.000000                                -0.697453                                 -0.689625                             -0.689631                                  -0.689605                              -0.689612                  -0.658209                        -0.707573                   -0.697451                   -0.702994
total_pledge_collateral_log_differenced                                  0.999641                          0.999641                                  0.999138                                0.999724                            0.999092                            0.999678                     0.872436                                   0.994398                                       0.999327                                      -0.697453                                 1.000000                                  0.999270                              0.999270                                   0.999271                               0.999271                   0.987408                         0.998150                    1.000000                    0.999390
total_qa_bytes_committed_log_differenced                                 0.999022                          0.999022                                  0.998602                                0.999087                            0.998562                            0.999058                     0.871857                                   0.994024                                       0.999799                                      -0.689625                                 0.999270                                  1.000000                              1.000000                                   1.000000                               1.000000                   0.986870                         0.997654                    0.999270                    0.998818
total_qa_bytes_power_log_differenced                                     0.999022                          0.999022                                  0.998602                                0.999087                            0.998562                            0.999058                     0.871852                                   0.994027                                       0.999799                                      -0.689631                                 0.999270                                  1.000000                              1.000000                                   1.000000                               1.000000                   0.986869                         0.997653                    0.999270                    0.998818
total_raw_bytes_committed_log_differenced                                0.999021                          0.999021                                  0.998599                                0.999086                            0.998559                            0.999056                     0.871825                                   0.994027                                       0.999799                                      -0.689605                                 0.999271                                  1.000000                              1.000000                                   1.000000                               1.000000                   0.986875                         0.997649                    0.999271                    0.998816
total_raw_bytes_power_log_differenced                                    0.999021                          0.999021                                  0.998599                                0.999086                            0.998559                            0.999056                     0.871822                                   0.994029                                       0.999799                                      -0.689612                                 0.999271                                  1.000000                              1.000000                                   1.000000                               1.000000                   0.986873                         0.997649                    0.999271                    0.998816
burnt_fil_log_differenced                                                0.984772                          0.984772                                  0.983129                                0.985118                            0.982996                            0.984918                     0.813834                                   0.986321                                       0.986356                                      -0.658209                                 0.987408                                  0.986870                              0.986869                                   0.986875                               0.986873                   1.000000                         0.979336                    0.987410                    0.983904
circulating_fil_log_differenced                                          0.999404                          0.999404                                  0.999780                                0.999285                            0.999799                            0.999356                     0.896486                                   0.990845                                       0.997831                                      -0.707573                                 0.998150                                  0.997654                              0.997653                                   0.997649                               0.997649                   0.979336                         1.000000                    0.998150                    0.999639
locked_fil_log_differenced                                               0.999641                          0.999641                                  0.999138                                0.999724                            0.999092                            0.999678                     0.872433                                   0.994398                                       0.999327                                      -0.697451                                 1.000000                                  0.999270                              0.999270                                   0.999271                               0.999271                   0.987410                         0.998150                    1.000000                    0.999390
vested_fil_log_differenced                                               0.999965                          0.999965                                  0.999977                                0.999930                            0.999969                            0.999952                     0.886212                                   0.992881                                       0.998924                                      -0.702994                                 0.999390                                  0.998818                              0.998818                                   0.998816                               0.998816                   0.983904                         0.999639                    0.999390                    1.000000

alpha = 0.05
result_dfs = []
variables = list(log_differenced_subset.columns)
for i in variables:
    for j in variables:
        if i==j:
            pass
        else:
            results_summary = results.test_causality(i,j, 
                                                     kind='f',signif=alpha).summary()


            df = pd.read_html(results_summary.as_html(),header=0, index_col=0)[0]
            df['alpha'] = alpha
            df['caused'] = i
            df['causing'] = j
            result_dfs.append(df)
        
Grangers_df = pd.concat(result_dfs)
Grangers_df.reset_index(inplace=True)
Grangers_df['result'] = Grangers_df['p-value'].apply(lambda x: 'reject H0' if x < alpha else 'fail to reject H0' )
Grangers_df

	Test statistic	Critical value	p-value	df	alpha	caused	causing	result
0	0.03640	2.372	0.997	(4, 1618382)	0.05	cum_sum_baseline_log_differenced	cum_sum_realized_log_differenced	fail to reject H0
1	15.70000	2.372	0.000	(4, 1618382)	0.05	cum_sum_baseline_log_differenced	effective_baseline_power_log_differenced	reject H0
2	10.82000	2.372	0.000	(4, 1618382)	0.05	cum_sum_baseline_log_differenced	effective_network_time_log_differenced	reject H0
3	0.03617	2.372	0.998	(4, 1618382)	0.05	cum_sum_baseline_log_differenced	new_baseline_power_log_differenced	fail to reject H0
4	12.99000	2.372	0.000	(4, 1618382)	0.05	cum_sum_baseline_log_differenced	total_mined_reward_log_differenced	reject H0
...	...	...	...	...	...	...	...	...
337	13.88000	2.372	0.000	(4, 1618382)	0.05	vested_fil_log_differenced	total_raw_bytes_committed_log_differenced	reject H0
338	10.37000	2.372	0.000	(4, 1618382)	0.05	vested_fil_log_differenced	total_raw_bytes_power_log_differenced	reject H0
339	12.33000	2.372	0.000	(4, 1618382)	0.05	vested_fil_log_differenced	burnt_fil_log_differenced	reject H0
340	12.45000	2.372	0.000	(4, 1618382)	0.05	vested_fil_log_differenced	circulating_fil_log_differenced	reject H0
341	16.49000	2.372	0.000	(4, 1618382)	0.05	vested_fil_log_differenced	locked_fil_log_differenced	reject H0

342 rows × 8 columns

heatdf = Grangers_df.pivot(index='caused', columns=['causing'],values=['p-value'])

f, ax = plt.subplots(figsize=(15, 12))
sns.heatmap(heatdf, annot=True, linewidths=.5, ax=ax,cmap=['green','red'],center=0.05)
plt.suptitle('Heatmap of Granger Casuality \n Green shows causal relationship whereas red shows no causal relationship')

Text(0.5, 0.98, 'Heatmap of Granger Casuality \n Green shows causal relationship whereas red shows no causal relationship')

Grangers_df.query("result == 'reject H0'").sort_values('p-value',ascending=True)

	Test statistic	Critical value	p-value	df	alpha	caused	causing	result
1	15.700	2.372	0.000	(4, 1618382)	0.05	cum_sum_baseline_log_differenced	effective_baseline_power_log_differenced	reject H0
205	21.850	2.372	0.000	(4, 1618382)	0.05	total_qa_bytes_committed_log_differenced	participating_miner_count_log_differenced	reject H0
206	15.130	2.372	0.000	(4, 1618382)	0.05	total_qa_bytes_committed_log_differenced	qa_smoothed_position_estimate_log_differenced	reject H0
208	14.970	2.372	0.000	(4, 1618382)	0.05	total_qa_bytes_committed_log_differenced	total_pledge_collateral_log_differenced	reject H0
209	8.921	2.372	0.000	(4, 1618382)	0.05	total_qa_bytes_committed_log_differenced	total_qa_bytes_power_log_differenced	reject H0
...	...	...	...	...	...	...	...	...
297	3.205	2.372	0.012	(4, 1618382)	0.05	circulating_fil_log_differenced	qa_smoothed_velocity_estimate_log_differenced	reject H0
269	3.224	2.372	0.012	(4, 1618382)	0.05	total_raw_bytes_power_log_differenced	vested_fil_log_differenced	reject H0
251	3.224	2.372	0.012	(4, 1618382)	0.05	total_raw_bytes_committed_log_differenced	vested_fil_log_differenced	reject H0
215	3.225	2.372	0.012	(4, 1618382)	0.05	total_qa_bytes_committed_log_differenced	vested_fil_log_differenced	reject H0
233	3.225	2.372	0.012	(4, 1618382)	0.05	total_qa_bytes_power_log_differenced	vested_fil_log_differenced	reject H0

305 rows × 8 columns