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ARIMA_summaries
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Full Timeframe - SPX:
ARIMA Model Results
==============================================================================
Dep. Variable: D.SPX No. Observations: 3126
Model: ARIMA(1, 4) Log Likelihood -5372.099
Method: css-mle S.D. of innovations 1.348
Date: Fri, 22 May 2020 AIC 10758.198
Time: 02:26:09 BIC 10800.531
Sample: 0 HQIC 10773.393
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const 2.142e-05 2.38e-05 0.899 0.369 -2.53e-05 6.81e-05
ar.L1.D.SPX -0.7491 0.111 -6.738 0.000 -0.967 -0.531
ma.L1.D.SPX -0.3817 0.112 -3.406 0.001 -0.601 -0.162
ma.L2.D.SPX -0.7094 0.126 -5.617 0.000 -0.957 -0.462
ma.L3.D.SPX 0.1256 0.021 6.079 0.000 0.085 0.166
ma.L4.D.SPX -0.0345 0.019 -1.780 0.075 -0.072 0.003
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -1.3349 +0.0000j 1.3349 0.5000
MA.1 1.0000 -0.0000j 1.0000 -0.0000
MA.2 -1.2672 -0.0000j 1.2672 -0.5000
MA.3 1.9552 -4.3668j 4.7846 -0.1830
MA.4 1.9552 +4.3668j 4.7846 0.1830
-----------------------------------------------------------------------------
Full Timeframe - VIX:
ARIMA Model Results
==============================================================================
Dep. Variable: D.VIX No. Observations: 3126
Model: ARIMA(3, 2) Log Likelihood -10937.514
Method: css-mle S.D. of innovations 7.993
Date: Fri, 22 May 2020 AIC 21889.028
Time: 02:26:38 BIC 21931.361
Sample: 0 HQIC 21904.223
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const 1.187e-05 0.000 0.085 0.933 -0.000 0.000
ar.L1.D.VIX -1.0407 0.077 -13.577 0.000 -1.191 -0.890
ar.L2.D.VIX -0.1265 0.027 -4.731 0.000 -0.179 -0.074
ar.L3.D.VIX -0.0310 0.019 -1.668 0.095 -0.067 0.005
ma.L1.D.VIX -0.0546 0.074 -0.733 0.463 -0.201 0.091
ma.L2.D.VIX -0.9454 0.074 -12.696 0.000 -1.091 -0.799
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -1.0624 -0.0000j 1.0624 -0.5000
AR.2 -1.5102 -5.3002j 5.5111 -0.2942
AR.3 -1.5102 +5.3002j 5.5111 0.2942
MA.1 1.0000 +0.0000j 1.0000 0.0000
MA.2 -1.0577 +0.0000j 1.0577 0.5000
-----------------------------------------------------------------------------
Full Timeframe - SSE:
ARIMA Model Results
==============================================================================
Dep. Variable: D.SSE No. Observations: 3126
Model: ARIMA(1, 5) Log Likelihood -6076.779
Method: css-mle S.D. of innovations 1.688
Date: Fri, 22 May 2020 AIC 12169.558
Time: 02:26:52 BIC 12217.938
Sample: 0 HQIC 12186.923
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const -2.734e-06 3.61e-05 -0.076 0.940 -7.35e-05 6.81e-05
ar.L1.D.SSE -0.3119 0.170 -1.830 0.067 -0.646 0.022
ma.L1.D.SSE -0.6940 0.170 -4.088 0.000 -1.027 -0.361
ma.L2.D.SSE -0.2975 0.171 -1.739 0.082 -0.633 0.038
ma.L3.D.SSE 0.0226 0.023 1.001 0.317 -0.022 0.067
ma.L4.D.SSE 0.0406 0.023 1.790 0.073 -0.004 0.085
ma.L5.D.SSE -0.0717 0.018 -4.009 0.000 -0.107 -0.037
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -3.2063 +0.0000j 3.2063 0.5000
MA.1 1.0000 -0.0000j 1.0000 -0.0000
MA.2 -1.4741 -1.0539j 1.8120 -0.4012
MA.3 -1.4741 +1.0539j 1.8120 0.4012
MA.4 1.2574 -1.6334j 2.0613 -0.1456
MA.5 1.2574 +1.6334j 2.0613 0.1456
-----------------------------------------------------------------------------
Full Timeframe - CNY:
ARIMA Model Results
==============================================================================
Dep. Variable: D.CNY No. Observations: 3126
Model: ARIMA(1, 1) Log Likelihood 505.770
Method: css-mle S.D. of innovations 0.206
Date: Fri, 22 May 2020 AIC -1003.540
Time: 02:26:56 BIC -979.350
Sample: 0 HQIC -994.857
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const -1.374e-05 3.63e-06 -3.783 0.000 -2.09e-05 -6.62e-06
ar.L1.D.CNY -0.1216 0.018 -6.851 0.000 -0.156 -0.087
ma.L1.D.CNY -1.0000 0.001 -975.481 0.000 -1.002 -0.998
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -8.2227 +0.0000j 8.2227 0.5000
MA.1 1.0000 +0.0000j 1.0000 0.0000
-----------------------------------------------------------------------------
Great Recession - SPX:
ARIMA Model Results
==============================================================================
Dep. Variable: D.SPX No. Observations: 371
Model: ARIMA(4, 2) Log Likelihood -861.800
Method: css-mle S.D. of innovations 2.448
Date: Fri, 22 May 2020 AIC 1739.600
Time: 02:26:58 BIC 1770.930
Sample: 0 HQIC 1752.043
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const 0.0006 0.001 0.658 0.511 -0.001 0.002
ar.L1.D.SPX 0.4697 0.541 0.869 0.385 -0.590 1.530
ar.L2.D.SPX -0.0969 0.082 -1.186 0.236 -0.257 0.063
ar.L3.D.SPX 0.1606 0.101 1.592 0.111 -0.037 0.358
ar.L4.D.SPX -0.0763 0.058 -1.313 0.189 -0.190 0.038
ma.L1.D.SPX -1.5737 0.541 -2.910 0.004 -2.634 -0.514
ma.L2.D.SPX 0.5737 0.541 1.061 0.289 -0.486 1.633
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -0.8060 -1.6437j 1.8307 -0.3226
AR.2 -0.8060 +1.6437j 1.8307 0.3226
AR.3 1.8579 -0.6756j 1.9770 -0.0555
AR.4 1.8579 +0.6756j 1.9770 0.0555
MA.1 1.0000 +0.0000j 1.0000 0.0000
MA.2 1.7431 +0.0000j 1.7431 0.0000
-----------------------------------------------------------------------------
Great Recession - VIX:
ARIMA Model Results
==============================================================================
Dep. Variable: D.VIX No. Observations: 371
Model: ARIMA(5, 2) Log Likelihood -1265.654
Method: css-mle S.D. of innovations 7.274
Date: Fri, 22 May 2020 AIC 2549.308
Time: 02:27:01 BIC 2584.554
Sample: 0 HQIC 2563.306
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const -0.0022 0.003 -0.652 0.514 -0.009 0.004
ar.L1.D.VIX 0.7474 nan nan nan nan nan
ar.L2.D.VIX 0.0221 0.064 0.347 0.729 -0.103 0.147
ar.L3.D.VIX 0.0578 0.064 0.902 0.367 -0.068 0.184
ar.L4.D.VIX 0.0144 0.064 0.224 0.823 -0.112 0.141
ar.L5.D.VIX 0.0565 0.051 1.098 0.272 -0.044 0.157
ma.L1.D.VIX -1.9002 nan nan nan nan nan
ma.L2.D.VIX 0.9002 nan nan nan nan nan
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 1.0741 -0.0000j 1.0741 -0.0000
AR.2 0.9092 -1.6659j 1.8979 -0.1705
AR.3 0.9092 +1.6659j 1.8979 0.1705
AR.4 -1.5737 -1.4475j 2.1382 -0.3816
AR.5 -1.5737 +1.4475j 2.1382 0.3816
MA.1 1.0000 +0.0000j 1.0000 0.0000
MA.2 1.1108 +0.0000j 1.1108 0.0000
-----------------------------------------------------------------------------
Great Recession - SSE:
ARIMA Model Results
==============================================================================
Dep. Variable: D.SSE No. Observations: 371
Model: ARIMA(2, 3) Log Likelihood -887.793
Method: css-mle S.D. of innovations 2.505
Date: Fri, 22 May 2020 AIC 1789.587
Time: 02:27:02 BIC 1817.000
Sample: 0 HQIC 1800.474
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const -0.0034 nan nan nan nan nan
ar.L1.D.SSE -0.6844 nan nan nan nan nan
ar.L2.D.SSE -0.9464 0.055 -17.344 0.000 -1.053 -0.839
ma.L1.D.SSE -0.2353 nan nan nan nan nan
ma.L2.D.SSE 0.3426 nan nan nan nan nan
ma.L3.D.SSE -1.0206 nan nan nan nan nan
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -0.3616 -0.9622j 1.0280 -0.3072
AR.2 -0.3616 +0.9622j 1.0280 0.3072
MA.1 -0.3482 -0.9100j 0.9743 -0.3082
MA.2 -0.3482 +0.9100j 0.9743 0.3082
MA.3 1.0321 -0.0000j 1.0321 -0.0000
-----------------------------------------------------------------------------
Great Recession - CNY:
ARIMA Model Results
==============================================================================
Dep. Variable: D.CNY No. Observations: 371
Model: ARIMA(5, 4) Log Likelihood 213.708
Method: css-mle S.D. of innovations 0.135
Date: Fri, 22 May 2020 AIC -405.416
Time: 02:27:03 BIC -362.338
Sample: 0 HQIC -388.307
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const -0.0002 0.000 -1.111 0.267 -0.000 0.000
ar.L1.D.CNY -1.4934 nan nan nan nan nan
ar.L2.D.CNY -1.0938 nan nan nan nan nan
ar.L3.D.CNY -0.7436 nan nan nan nan nan
ar.L4.D.CNY -0.2468 0.105 -2.359 0.018 -0.452 -0.042
ar.L5.D.CNY -0.1021 0.070 -1.452 0.147 -0.240 0.036
ma.L1.D.CNY 0.4359 nan nan nan nan nan
ma.L2.D.CNY -0.5157 nan nan nan nan nan
ma.L3.D.CNY -0.3975 nan nan nan nan nan
ma.L4.D.CNY -0.4382 nan nan nan nan nan
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -1.0014 -0.0000j 1.0014 -0.5000
AR.2 -0.8293 -1.4953j 1.7099 -0.3306
AR.3 -0.8293 +1.4953j 1.7099 0.3306
AR.4 0.1214 -1.8252j 1.8292 -0.2394
AR.5 0.1214 +1.8252j 1.8292 0.2394
MA.1 1.0232 -0.0000j 1.0232 -0.0000
MA.2 -1.0038 -0.0000j 1.0038 -0.5000
MA.3 -0.4633 -1.4168j 1.4906 -0.3003
MA.4 -0.4633 +1.4168j 1.4906 0.3003
-----------------------------------------------------------------------------
COVID-19 Recession - SPX:
ARIMA Model Results
==============================================================================
Dep. Variable: D2.SPX No. Observations: 94
Model: ARIMA(4, 1) Log Likelihood -258.943
Method: css-mle S.D. of innovations 3.582
Date: Fri, 22 May 2020 AIC 531.887
Time: 02:27:04 BIC 549.690
Sample: 0 HQIC 539.078
================================================================================
coef std err z P>|z| [0.025 0.975]
--------------------------------------------------------------------------------
const 0.0001 0.003 0.049 0.961 -0.005 0.005
ar.L1.D2.SPX -1.7166 0.094 -18.178 0.000 -1.902 -1.532
ar.L2.D2.SPX -1.5513 0.176 -8.822 0.000 -1.896 -1.207
ar.L3.D2.SPX -0.9229 0.175 -5.283 0.000 -1.265 -0.581
ar.L4.D2.SPX -0.3749 0.093 -4.039 0.000 -0.557 -0.193
ma.L1.D2.SPX -1.0000 0.028 -36.141 0.000 -1.054 -0.946
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -1.0327 -0.5457j 1.1680 -0.4226
AR.2 -1.0327 +0.5457j 1.1680 0.4226
AR.3 -0.1981 -1.3842j 1.3983 -0.2726
AR.4 -0.1981 +1.3842j 1.3983 0.2726
MA.1 1.0000 +0.0000j 1.0000 0.0000
-----------------------------------------------------------------------------
COVID-19 Recession - VIX:
ARIMA Model Results
==============================================================================
Dep. Variable: D.VIX No. Observations: 95
Model: ARIMA(4, 4) Log Likelihood -363.018
Method: css-mle S.D. of innovations 8.903
Date: Fri, 22 May 2020 AIC 746.035
Time: 02:27:05 BIC 771.574
Sample: 0 HQIC 756.355
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const -0.0408 0.113 -0.361 0.718 -0.262 0.180
ar.L1.D.VIX -0.4649 0.200 -2.323 0.020 -0.857 -0.073
ar.L2.D.VIX -0.4727 0.162 -2.916 0.004 -0.790 -0.155
ar.L3.D.VIX -0.7139 0.157 -4.549 0.000 -1.021 -0.406
ar.L4.D.VIX -0.2247 0.120 -1.874 0.061 -0.460 0.010
ma.L1.D.VIX -0.3210 0.243 -1.320 0.187 -0.798 0.156
ma.L2.D.VIX -0.2751 0.342 -0.805 0.421 -0.945 0.395
ma.L3.D.VIX 0.9941 0.362 2.745 0.006 0.284 1.704
ma.L4.D.VIX -1.0776 0.214 -5.030 0.000 -1.497 -0.658
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 0.3580 -1.0395j 1.0994 -0.1972
AR.2 0.3580 +1.0395j 1.0994 0.1972
AR.3 -1.6200 -0.0000j 1.6200 -0.5000
AR.4 -2.2729 -0.0000j 2.2729 -0.5000
MA.1 -0.8294 -0.0000j 0.8294 -0.5000
MA.2 0.3165 -0.9486j 1.0000 -0.1987
MA.3 0.3165 +0.9486j 1.0000 0.1987
MA.4 1.1189 -0.0000j 1.1189 -0.0000
-----------------------------------------------------------------------------
COVID-19 Recession - SSE:
ARIMA Model Results
==============================================================================
Dep. Variable: D.SSE No. Observations: 95
Model: ARIMA(5, 1) Log Likelihood -174.305
Method: css-mle S.D. of innovations 1.479
Date: Fri, 22 May 2020 AIC 364.611
Time: 02:27:06 BIC 385.042
Sample: 0 HQIC 372.866
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const -0.0022 0.005 -0.406 0.684 -0.013 0.008
ar.L1.D.SSE -0.0134 0.103 -0.130 0.897 -0.215 0.189
ar.L2.D.SSE 0.0553 0.102 0.542 0.588 -0.144 0.255
ar.L3.D.SSE 0.0502 0.101 0.496 0.620 -0.148 0.248
ar.L4.D.SSE -0.1287 0.101 -1.279 0.201 -0.326 0.069
ar.L5.D.SSE 0.0138 0.101 0.136 0.892 -0.185 0.213
ma.L1.D.SSE -1.0000 0.033 -29.946 0.000 -1.065 -0.935
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -1.1306 -1.0719j 1.5580 -0.3792
AR.2 -1.1306 +1.0719j 1.5580 0.3792
AR.3 1.3542 -1.2361j 1.8335 -0.1178
AR.4 1.3542 +1.2361j 1.8335 0.1178
AR.5 8.8836 -0.0000j 8.8836 -0.0000
MA.1 1.0000 +0.0000j 1.0000 0.0000
-----------------------------------------------------------------------------
COVID-19 Recession - CNY:
ARIMA Model Results
==============================================================================
Dep. Variable: D.CNY No. Observations: 95
Model: ARIMA(2, 3) Log Likelihood -29.207
Method: css-mle S.D. of innovations 0.318
Date: Fri, 22 May 2020 AIC 72.413
Time: 02:27:09 BIC 90.290
Sample: 0 HQIC 79.637
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const -0.0008 0.001 -0.686 0.493 -0.003 0.002
ar.L1.D.CNY -0.6477 0.147 -4.400 0.000 -0.936 -0.359
ar.L2.D.CNY -0.9421 0.054 -17.306 0.000 -1.049 -0.835
ma.L1.D.CNY -0.3082 0.122 -2.520 0.012 -0.548 -0.068
ma.L2.D.CNY 0.3082 0.126 2.443 0.015 0.061 0.555
ma.L3.D.CNY -1.0000 0.073 -13.661 0.000 -1.143 -0.857
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -0.3437 -0.9712j 1.0303 -0.3041
AR.2 -0.3437 +0.9712j 1.0303 0.3041
MA.1 1.0000 -0.0000j 1.0000 -0.0000
MA.2 -0.3459 -0.9383j 1.0000 -0.3062
MA.3 -0.3459 +0.9383j 1.0000 0.3062
-----------------------------------------------------------------------------