MA, AR, and Arma
introml.analyticsdojo.com
60. MA, AR, and Arma#
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.pylab import rcParams
rcParams['figure.figsize'] = 15, 5
import seaborn as sns
!pip -q install yfinance
import yfinance as yf
####Moving Average analysis
FB = yf.Ticker("META")
# get historical market data
FB_values = FB.history(start="2020-06-01")
FB_values[['Close']].plot(lw=2)
<AxesSubplot:xlabel='Date'>
#Rolling average
FB_values['rolling_av'] = FB_values['Close'].rolling(10).mean()
# take a look
FB_values[['Close','rolling_av']].plot(lw=2)
<AxesSubplot:xlabel='Date'>
from statsmodels.tsa.arima.model import ARIMA
ARMA_model = ARIMA(endog=FB_values['Close'], order=(0, 0, 10))
results = ARMA_model.fit()
print(results.summary())
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:581: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
warnings.warn('A date index has been provided, but it has no'
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:581: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
warnings.warn('A date index has been provided, but it has no'
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:581: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
warnings.warn('A date index has been provided, but it has no'
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
warn('Non-invertible starting MA parameters found.'
SARIMAX Results
==============================================================================
Dep. Variable: Close No. Observations: 608
Model: ARIMA(0, 0, 10) Log Likelihood -2709.211
Date: Wed, 26 Oct 2022 AIC 5442.423
Time: 19:26:34 BIC 5495.345
Sample: 0 HQIC 5463.012
- 608
Covariance Type: opg
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 263.6635 7.284 36.199 0.000 249.388 277.939
ma.L1 0.7786 0.019 40.264 0.000 0.741 0.817
ma.L2 0.3297 0.013 24.505 0.000 0.303 0.356
ma.L3 0.1467 0.011 12.936 0.000 0.125 0.169
ma.L4 0.9416 0.011 87.808 0.000 0.921 0.963
ma.L5 1.0996 0.019 59.397 0.000 1.063 1.136
ma.L6 0.8785 0.020 44.231 0.000 0.840 0.917
ma.L7 0.1297 0.013 10.040 0.000 0.104 0.155
ma.L8 0.3853 0.013 29.529 0.000 0.360 0.411
ma.L9 0.8021 0.015 53.684 0.000 0.773 0.831
ma.L10 0.8761 0.019 46.821 0.000 0.839 0.913
sigma2 439.7564 29.343 14.987 0.000 382.245 497.268
===================================================================================
Ljung-Box (L1) (Q): 224.32 Jarque-Bera (JB): 19.29
Prob(Q): 0.00 Prob(JB): 0.00
Heteroskedasticity (H): 6.97 Skew: -0.39
Prob(H) (two-sided): 0.00 Kurtosis: 3.40
===================================================================================
Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/base/model.py:566: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
warnings.warn("Maximum Likelihood optimization failed to "
start_date = '2020-06-12'
end_date = '2022-10-04'
FB_values['forecast_Ma'] = results.predict(start=start_date, end=end_date)
FB_values[['Close','rolling_av','forecast_Ma']].plot(lw=2)
<AxesSubplot:xlabel='Date'>
# A Mojaor flaw is that the time series may not be stationary. It has to be done on returns
####Auto Regressive analysis
ARMA_model = ARIMA(endog=FB_values['Close'], order=(10, 0,0))
results = ARMA_model.fit()
print(results.summary())
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:581: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
warnings.warn('A date index has been provided, but it has no'
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:581: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
warnings.warn('A date index has been provided, but it has no'
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:581: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
warnings.warn('A date index has been provided, but it has no'
SARIMAX Results
==============================================================================
Dep. Variable: Close No. Observations: 608
Model: ARIMA(10, 0, 0) Log Likelihood -2051.121
Date: Wed, 26 Oct 2022 AIC 4126.243
Time: 19:26:35 BIC 4179.165
Sample: 0 HQIC 4146.832
- 608
Covariance Type: opg
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 263.6740 509.998 0.517 0.605 -735.904 1263.252
ar.L1 0.9530 0.050 18.994 0.000 0.855 1.051
ar.L2 0.0623 0.062 1.004 0.315 -0.059 0.184
ar.L3 -0.1102 0.053 -2.090 0.037 -0.214 -0.007
ar.L4 0.0396 0.051 0.768 0.442 -0.061 0.140
ar.L5 0.0193 0.054 0.355 0.722 -0.087 0.126
ar.L6 0.0225 0.056 0.399 0.690 -0.088 0.133
ar.L7 -0.0239 0.057 -0.422 0.673 -0.135 0.087
ar.L8 0.0016 0.070 0.022 0.982 -0.136 0.139
ar.L9 0.0922 0.076 1.211 0.226 -0.057 0.242
ar.L10 -0.0570 0.053 -1.072 0.284 -0.161 0.047
sigma2 49.3269 1.286 38.352 0.000 46.806 51.848
===================================================================================
Ljung-Box (L1) (Q): 0.00 Jarque-Bera (JB): 26048.16
Prob(Q): 0.96 Prob(JB): 0.00
Heteroskedasticity (H): 2.02 Skew: -2.53
Prob(H) (two-sided): 0.00 Kurtosis: 34.66
===================================================================================
Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
start_date = '2020-06-12'
end_date = '2022-10-04'
FB_values['forecast_Ar'] = results.predict(start=start_date, end=end_date)
FB_values[['Close','rolling_av','forecast_Ma','forecast_Ar']].plot(lw=2)
<AxesSubplot:xlabel='Date'>
####Now lets do AR & MA
ARMA_model = ARIMA(endog=FB_values['Close'], order=(10, 0,10))
results = ARMA_model.fit()
print(results.summary())
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:581: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
warnings.warn('A date index has been provided, but it has no'
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:581: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
warnings.warn('A date index has been provided, but it has no'
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:581: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
warnings.warn('A date index has been provided, but it has no'
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
warn('Non-stationary starting autoregressive parameters'
SARIMAX Results
==============================================================================
Dep. Variable: Close No. Observations: 608
Model: ARIMA(10, 0, 10) Log Likelihood -2048.853
Date: Wed, 26 Oct 2022 AIC 4141.706
Time: 19:26:37 BIC 4238.730
Sample: 0 HQIC 4179.453
- 608
Covariance Type: opg
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 263.6608 77.496 3.402 0.001 111.771 415.551
ar.L1 0.3242 10.387 0.031 0.975 -20.035 20.683
ar.L2 0.6924 8.735 0.079 0.937 -16.428 17.813
ar.L3 -0.0474 2.440 -0.019 0.985 -4.830 4.735
ar.L4 -0.4487 1.723 -0.260 0.795 -3.826 2.929
ar.L5 0.0365 3.563 0.010 0.992 -6.946 7.019
ar.L6 0.3317 2.301 0.144 0.885 -4.179 4.842
ar.L7 -0.1589 2.141 -0.074 0.941 -4.355 4.037
ar.L8 -0.4674 2.951 -0.158 0.874 -6.252 5.317
ar.L9 0.4247 3.224 0.132 0.895 -5.893 6.743
ar.L10 0.2979 6.117 0.049 0.961 -11.692 12.288
ma.L1 0.6286 10.385 0.061 0.952 -19.726 20.984
ma.L2 -0.0274 1.333 -0.021 0.984 -2.639 2.585
ma.L3 -0.0354 0.766 -0.046 0.963 -1.537 1.466
ma.L4 0.3989 0.523 0.762 0.446 -0.627 1.424
ma.L5 0.4050 3.963 0.102 0.919 -7.362 8.172
ma.L6 0.1198 2.022 0.059 0.953 -3.844 4.083
ma.L7 0.2405 0.631 0.381 0.703 -0.997 1.478
ma.L8 0.6664 2.667 0.250 0.803 -4.561 5.893
ma.L9 0.3085 5.696 0.054 0.957 -10.855 11.472
ma.L10 0.0216 0.318 0.068 0.946 -0.601 0.645
sigma2 49.3105 1.759 28.029 0.000 45.862 52.759
===================================================================================
Ljung-Box (L1) (Q): 0.00 Jarque-Bera (JB): 25080.34
Prob(Q): 0.97 Prob(JB): 0.00
Heteroskedasticity (H): 1.99 Skew: -2.45
Prob(H) (two-sided): 0.00 Kurtosis: 34.08
===================================================================================
Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
/opt/anaconda3/lib/python3.8/site-packages/statsmodels/base/model.py:566: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
warnings.warn("Maximum Likelihood optimization failed to "
start_date = '2020-06-12'
end_date = '2022-10-04'
FB_values['forecast_ArMA'] = results.predict(start=start_date, end=end_date)
plt.rcParams["figure.figsize"] = (15,10)
sns.set(font_scale=2)
FB_values[['Close','forecast_Ar','forecast_ArMA']].plot(lw=2)
<AxesSubplot:xlabel='Date'>
