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ARIMA_max10
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Full Timeframe - SPX
ARIMA(8,0,8) - AIC: 10706.840412480784
ARMA Model Results
==============================================================================
Dep. Variable: SPX No. Observations: 3127
Model: ARMA(8, 8) Log Likelihood -5335.420
Method: css-mle S.D. of innovations 1.333
Date: Sat, 23 May 2020 AIC 10706.840
Time: 17:27:29 BIC 10815.701
Sample: 0 HQIC 10745.915
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0298 0.021 1.430 0.153 -0.011 0.071
ar.L1.SPX 0.5922 0.449 1.319 0.187 -0.288 1.472
ar.L2.SPX -0.0488 0.303 -0.161 0.872 -0.642 0.545
ar.L3.SPX 0.1350 0.232 0.582 0.560 -0.319 0.589
ar.L4.SPX -0.5259 0.160 -3.283 0.001 -0.840 -0.212
ar.L5.SPX -0.1749 0.183 -0.956 0.339 -0.533 0.184
ar.L6.SPX 0.2696 0.297 0.909 0.363 -0.312 0.851
ar.L7.SPX 0.3441 0.493 0.698 0.485 -0.623 1.311
ar.L8.SPX -0.5385 0.187 -2.874 0.004 -0.906 -0.171
ma.L1.SPX -0.7251 0.446 -1.625 0.104 -1.600 0.150
ma.L2.SPX 0.1472 0.367 0.401 0.688 -0.572 0.867
ma.L3.SPX -0.1528 0.224 -0.682 0.495 -0.592 0.286
ma.L4.SPX 0.5144 0.197 2.611 0.009 0.128 0.901
ma.L5.SPX 0.1106 0.233 0.475 0.635 -0.346 0.567
ma.L6.SPX -0.3111 0.329 -0.946 0.344 -0.956 0.333
ma.L7.SPX -0.2670 0.548 -0.487 0.626 -1.341 0.807
ma.L8.SPX 0.5097 0.129 3.946 0.000 0.256 0.763
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -1.0246 -0.5127j 1.1457 -0.4262
AR.2 -1.0246 +0.5127j 1.1457 0.4262
AR.3 -0.3627 -0.9414j 1.0089 -0.3085
AR.4 -0.3627 +0.9414j 1.0089 0.3085
AR.5 0.6793 -0.8063j 1.0543 -0.1386
AR.6 0.6793 +0.8063j 1.0543 0.1386
AR.7 1.0275 -0.4409j 1.1181 -0.0645
AR.8 1.0275 +0.4409j 1.1181 0.0645
MA.1 -1.0670 -0.5393j 1.1955 -0.4255
MA.2 -1.0670 +0.5393j 1.1955 0.4255
MA.3 -0.3602 -0.9549j 1.0206 -0.3074
MA.4 -0.3602 +0.9549j 1.0206 0.3074
MA.5 0.6646 -0.7991j 1.0394 -0.1396
MA.6 0.6646 +0.7991j 1.0394 0.1396
MA.7 1.0244 -0.4131j 1.1046 -0.0610
MA.8 1.0244 +0.4131j 1.1046 0.0610
-----------------------------------------------------------------------------
Full Timeframe - SSE
ARIMA(9,0,7) - AIC: 12169.41590258502
ARMA Model Results
==============================================================================
Dep. Variable: SSE No. Observations: 3127
Model: ARMA(9, 7) Log Likelihood -6066.708
Method: css-mle S.D. of innovations 1.684
Date: Sat, 23 May 2020 AIC 12169.416
Time: 17:29:23 BIC 12278.277
Sample: 0 HQIC 12208.490
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0287 0.032 0.885 0.376 -0.035 0.092
ar.L1.SSE -0.2747 nan nan nan nan nan
ar.L2.SSE -0.0892 nan nan nan nan nan
ar.L3.SSE 0.4280 nan nan nan nan nan
ar.L4.SSE 0.1717 nan nan nan nan nan
ar.L5.SSE -0.5307 nan nan nan nan nan
ar.L6.SSE -0.2641 0.066 -4.011 0.000 -0.393 -0.135
ar.L7.SSE -0.6699 nan nan nan nan nan
ar.L8.SSE 0.0598 nan nan nan nan nan
ar.L9.SSE 0.0762 nan nan nan nan nan
ma.L1.SSE 0.2732 nan nan nan nan nan
ma.L2.SSE 0.1061 nan nan nan nan nan
ma.L3.SSE -0.3794 nan nan nan nan nan
ma.L4.SSE -0.1136 nan nan nan nan nan
ma.L5.SSE 0.4993 nan nan nan nan nan
ma.L6.SSE 0.1966 0.062 3.167 0.002 0.075 0.318
ma.L7.SSE 0.6783 nan nan nan nan nan
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 0.8952 -0.4675j 1.0099 -0.0766
AR.2 0.8952 +0.4675j 1.0099 0.0766
AR.3 -1.0277 -0.0000j 1.0277 -0.5000
AR.4 -0.5448 -0.8494j 1.0091 -0.3408
AR.5 -0.5448 +0.8494j 1.0091 0.3408
AR.6 -0.0195 -1.1313j 1.1315 -0.2527
AR.7 -0.0195 +1.1313j 1.1315 0.2527
AR.8 2.8964 -0.0000j 2.8964 -0.0000
AR.9 -3.3143 -0.0000j 3.3143 -0.5000
MA.1 0.8974 -0.4625j 1.0096 -0.0757
MA.2 0.8974 +0.4625j 1.0096 0.0757
MA.3 -1.0204 -0.0000j 1.0204 -0.5000
MA.4 -0.5494 -0.8466j 1.0092 -0.3416
MA.5 -0.5494 +0.8466j 1.0092 0.3416
MA.6 0.0172 -1.1796j 1.1797 -0.2477
MA.7 0.0172 +1.1796j 1.1797 0.2477
-----------------------------------------------------------------------------
Full Timeframe - CNY
ARIMA(3,0,2) - AIC: -1011.603848904977
ARMA Model Results
==============================================================================
Dep. Variable: CNY No. Observations: 3127
Model: ARMA(3, 2) Log Likelihood 512.802
Method: css-mle S.D. of innovations 0.205
Date: Sat, 23 May 2020 AIC -1011.604
Time: 17:31:21 BIC -969.269
Sample: 0 HQIC -996.408
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0007 0.005 0.142 0.887 -0.009 0.010
ar.L1.CNY 0.2920 nan nan nan nan nan
ar.L2.CNY 0.5506 nan nan nan nan nan
ar.L3.CNY 0.0794 nan nan nan nan nan
ma.L1.CNY -0.4017 nan nan nan nan nan
ma.L2.CNY -0.5011 nan nan nan nan nan
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 1.0467 +0.0000j 1.0467 0.0000
AR.2 -2.0177 +0.0000j 2.0177 0.5000
AR.3 -5.9619 +0.0000j 5.9619 0.5000
MA.1 1.0676 +0.0000j 1.0676 0.0000
MA.2 -1.8692 +0.0000j 1.8692 0.5000
-----------------------------------------------------------------------------
COVID-19 Recession - SPX
ARIMA(6,1,1) - AIC: 504.22882175122317
ARIMA Model Results
==============================================================================
Dep. Variable: D.SPX No. Observations: 95
Model: ARIMA(6, 1) Log Likelihood -243.114
Method: css-mle S.D. of innovations 2.637
Date: Sat, 23 May 2020 AIC 504.229
Time: 17:31:26 BIC 527.214
Sample: 0 HQIC 513.516
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
const -0.0014 0.005 -0.259 0.796 -0.012 0.009
ar.L1.D.SPX -1.2145 0.087 -13.945 0.000 -1.385 -1.044
ar.L2.D.SPX -1.0125 0.140 -7.247 0.000 -1.286 -0.739
ar.L3.D.SPX -0.8637 0.158 -5.458 0.000 -1.174 -0.553
ar.L4.D.SPX -0.9828 0.156 -6.311 0.000 -1.288 -0.678
ar.L5.D.SPX -0.7841 0.137 -5.744 0.000 -1.052 -0.517
ar.L6.D.SPX -0.5923 0.089 -6.684 0.000 -0.766 -0.419
ma.L1.D.SPX -1.1256 nan nan nan nan nan
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 0.6419 -0.8757j 1.0858 -0.1493
AR.2 0.6419 +0.8757j 1.0858 0.1493
AR.3 -0.9179 -0.4660j 1.0294 -0.4252
AR.4 -0.9179 +0.4660j 1.0294 0.4252
AR.5 -0.3860 -1.0967j 1.1626 -0.3039
AR.6 -0.3860 +1.0967j 1.1626 0.3039
MA.1 0.8884 +0.0000j 0.8884 0.0000
-----------------------------------------------------------------------------
COVID-19 Recession - SSE
ARIMA(8,0,6) - AIC: 369.1476713571644
ARMA Model Results
==============================================================================
Dep. Variable: SSE No. Observations: 96
Model: ARMA(8, 6) Log Likelihood -168.574
Method: css-mle S.D. of innovations 1.340
Date: Sat, 23 May 2020 AIC 369.148
Time: 17:32:25 BIC 410.177
Sample: 0 HQIC 385.732
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const -0.0788 0.029 -2.751 0.006 -0.135 -0.023
ar.L1.SSE 0.4017 0.149 2.698 0.007 0.110 0.694
ar.L2.SSE 0.1174 0.144 0.816 0.415 -0.165 0.399
ar.L3.SSE 0.7575 0.155 4.872 0.000 0.453 1.062
ar.L4.SSE 0.0556 0.151 0.368 0.713 -0.241 0.352
ar.L5.SSE 0.3513 0.185 1.896 0.058 -0.012 0.714
ar.L6.SSE -0.7532 0.119 -6.320 0.000 -0.987 -0.520
ar.L7.SSE -0.0908 0.127 -0.715 0.475 -0.340 0.158
ar.L8.SSE 0.0834 0.116 0.718 0.473 -0.144 0.311
ma.L1.SSE -0.4874 0.129 -3.771 0.000 -0.741 -0.234
ma.L2.SSE -0.1065 0.144 -0.741 0.459 -0.388 0.175
ma.L3.SSE -0.8074 0.146 -5.522 0.000 -1.094 -0.521
ma.L4.SSE -0.1598 0.157 -1.016 0.309 -0.468 0.148
ma.L5.SSE -0.3839 0.169 -2.268 0.023 -0.716 -0.052
ma.L6.SSE 0.9488 0.152 6.225 0.000 0.650 1.247
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 -0.7848 -0.6771j 1.0365 -0.3867
AR.2 -0.7848 +0.6771j 1.0365 0.3867
AR.3 0.0174 -1.0378j 1.0379 -0.2473
AR.4 0.0174 +1.0378j 1.0379 0.2473
AR.5 1.0489 -0.1079j 1.0545 -0.0163
AR.6 1.0489 +0.1079j 1.0545 0.0163
AR.7 -2.8011 -0.0000j 2.8011 -0.5000
AR.8 3.3276 -0.0000j 3.3276 -0.0000
MA.1 -0.8078 -0.6336j 1.0266 -0.3942
MA.2 -0.8078 +0.6336j 1.0266 0.3942
MA.3 0.0104 -0.9999j 1.0000 -0.2483
MA.4 0.0104 +0.9999j 1.0000 0.2483
MA.5 0.9997 -0.0235j 1.0000 -0.0037
MA.6 0.9997 +0.0235j 1.0000 0.0037
-----------------------------------------------------------------------------
COVID-19 Recession - CNY
ARIMA(3,0,3) - AIC: 75.57924674406374
ARMA Model Results
==============================================================================
Dep. Variable: CNY No. Observations: 96
Model: ARMA(3, 3) Log Likelihood -29.790
Method: css-mle S.D. of innovations 0.257
Date: Sat, 23 May 2020 AIC 75.579
Time: 17:32:52 BIC 96.094
Sample: 0 HQIC 83.872
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0238 0.034 0.711 0.477 -0.042 0.090
ar.L1.CNY -0.0611 nan nan nan nan nan
ar.L2.CNY -0.3473 0.126 -2.761 0.006 -0.594 -0.101
ar.L3.CNY -0.6324 nan nan nan nan nan
ma.L1.CNY -0.0684 0.261 -0.262 0.794 -0.581 0.444
ma.L2.CNY 0.5509 nan nan nan nan nan
ma.L3.CNY 1.0508 nan nan nan nan nan
Roots
=============================================================================
Real Imaginary Modulus Frequency
-----------------------------------------------------------------------------
AR.1 0.3994 -1.0068j 1.0831 -0.1899
AR.2 0.3994 +1.0068j 1.0831 0.1899
AR.3 -1.3478 -0.0000j 1.3478 -0.5000
MA.1 0.3471 -0.8127j 0.8837 -0.1857
MA.2 0.3471 +0.8127j 0.8837 0.1857
MA.3 -1.2185 -0.0000j 1.2185 -0.5000
-----------------------------------------------------------------------------