VAR Study: TAIEX vs. Other Variables
2024-09-14. 基於 Vector Autoregressions ( Christopher A.Sims) 模型, 進行VAR模擬, 先以 TAIEX為目標作 VAR 分析
Cooper Future : NYMEX 銅期貨價格
Heatmap
Plot
S&P 500,TAIEX, and Copper
ADF Test: Copper
ADF Test Statistic -1.932388
p-value 0.316981
#Lags Used 25.000000
Number of Observations Used 5663.000000
Critical Value (1%) -3.431505
Critical Value (5%) -2.862051
Critical Value (10%) -2.567042
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ADF Test: S&P 500
ADF Test Statistic 2.410000
p-value 0.999015
#Lags Used 33.000000
Number of Observations Used 5655.000000
Critical Value (1%) -3.431507
Critical Value (5%) -2.862051
Critical Value (10%) -2.567042
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ADF Test: TAIEX
ADF Test Statistic 0.798213
p-value 0.991607
#Lags Used 19.000000
Number of Observations Used 5669.000000
Critical Value (1%) -3.431504
Critical Value (5%) -2.862050
Critical Value (10%) -2.567041
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/usr/local/lib/python3.10/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
self._init_dates(dates, freq)
VAR Order Selection (* highlights the minimums)
==================================================
AIC BIC FPE HQIC
--------------------------------------------------
0 10.02 10.02 2.242e+04 10.02
1 9.799 9.813* 1.802e+04 9.804
2 9.791 9.816 1.787e+04 9.800
3 9.787 9.822 1.780e+04 9.799*
4 9.788 9.834 1.782e+04 9.804
5 9.784 9.841 1.775e+04 9.804
6 9.784 9.851 1.774e+04 9.807
7 9.782 9.859 1.771e+04 9.809
8 9.781 9.869 1.770e+04 9.812
9 9.778 9.877 1.765e+04 9.813
10 9.779 9.888 1.767e+04 9.817
11 9.777* 9.897 1.763e+04* 9.819
12 9.779 9.909 1.766e+04 9.824
13 9.777 9.918 1.763e+04 9.826
14 9.778 9.929 1.764e+04 9.830
15 9.777 9.939 1.763e+04 9.834
--------------------------------------------------
Optimal lag length (based on AIC): 11
Summary of Regression Results
==================================
Model: VAR
Method: OLS
Date: Thu, 12, Sep, 2024
Time: 09:15:58
--------------------------------------------------------------------
No. of Equations: 3.00000 BIC: 9.89697
Nobs: 5677.00 HQIC: 9.81917
Log likelihood: -51817.6 FPE: 17634.2
AIC: 9.77759 Det(Omega_mle): 17321.1
--------------------------------------------------------------------
Results for equation Copper
==============================================================================
coefficient std. error t-stat prob
------------------------------------------------------------------------------
const 0.000369 0.000668 0.552 0.581
L1.Copper -0.084447 0.013816 -6.112 0.000
L1.S&P 500 0.000168 0.000027 6.293 0.000
L1.TAIEX 0.000005 0.000006 0.838 0.402
L2.Copper -0.003673 0.013926 -0.264 0.792
L2.S&P 500 0.000023 0.000029 0.777 0.437
L2.TAIEX 0.000017 0.000006 2.666 0.008
L3.Copper 0.013719 0.013921 0.986 0.324
L3.S&P 500 -0.000070 0.000030 -2.362 0.018
L3.TAIEX 0.000011 0.000007 1.737 0.082
L4.Copper 0.000815 0.013922 0.059 0.953
L4.S&P 500 0.000009 0.000030 0.312 0.755
L4.TAIEX -0.000004 0.000007 -0.585 0.559
L5.Copper -0.022717 0.013918 -1.632 0.103
L5.S&P 500 0.000059 0.000030 1.996 0.046
L5.TAIEX -0.000002 0.000007 -0.380 0.704
L6.Copper 0.000562 0.013925 0.040 0.968
L6.S&P 500 -0.000036 0.000030 -1.206 0.228
L6.TAIEX 0.000008 0.000007 1.212 0.225
L7.Copper 0.006853 0.013928 0.492 0.623
L7.S&P 500 0.000007 0.000030 0.231 0.818
L7.TAIEX 0.000015 0.000007 2.240 0.025
L8.Copper 0.022824 0.013931 1.638 0.101
L8.S&P 500 -0.000034 0.000030 -1.133 0.257
L8.TAIEX -0.000001 0.000007 -0.200 0.842
L9.Copper -0.004958 0.013921 -0.356 0.722
L9.S&P 500 -0.000030 0.000030 -0.999 0.318
L9.TAIEX -0.000009 0.000007 -1.320 0.187
L10.Copper 0.005258 0.013915 0.378 0.706
L10.S&P 500 0.000020 0.000030 0.681 0.496
L10.TAIEX 0.000003 0.000006 0.436 0.663
L11.Copper 0.009044 0.013848 0.653 0.514
L11.S&P 500 0.000018 0.000029 0.631 0.528
L11.TAIEX 0.000003 0.000006 0.558 0.577
==============================================================================
Results for equation S&P 500
==============================================================================
coefficient std. error t-stat prob
------------------------------------------------------------------------------
const 0.742552 0.349869 2.122 0.034
L1.Copper -3.379820 7.236568 -0.467 0.640
L1.S&P 500 -0.085555 0.014022 -6.102 0.000
L1.TAIEX -0.000609 0.003383 -0.180 0.857
L2.Copper 5.726605 7.294039 0.785 0.432
L2.S&P 500 0.031914 0.015441 2.067 0.039
L2.TAIEX 0.000983 0.003400 0.289 0.773
L3.Copper 6.759446 7.291304 0.927 0.354
L3.S&P 500 -0.003738 0.015490 -0.241 0.809
L3.TAIEX -0.000048 0.003411 -0.014 0.989
L4.Copper 3.026094 7.291729 0.415 0.678
L4.S&P 500 -0.038558 0.015521 -2.484 0.013
L4.TAIEX 0.000539 0.003411 0.158 0.875
L5.Copper -14.771486 7.289567 -2.026 0.043
L5.S&P 500 0.034417 0.015514 2.218 0.027
L5.TAIEX 0.003468 0.003429 1.011 0.312
L6.Copper -14.739776 7.293202 -2.021 0.043
L6.S&P 500 -0.036809 0.015515 -2.372 0.018
L6.TAIEX -0.000091 0.003432 -0.026 0.979
L7.Copper -6.322053 7.294790 -0.867 0.386
L7.S&P 500 0.055219 0.015528 3.556 0.000
L7.TAIEX 0.000166 0.003425 0.048 0.961
L8.Copper -1.144443 7.296627 -0.157 0.875
L8.S&P 500 -0.024724 0.015522 -1.593 0.111
L8.TAIEX -0.009476 0.003425 -2.767 0.006
L9.Copper -6.190974 7.291350 -0.849 0.396
L9.S&P 500 0.067708 0.015526 4.361 0.000
L9.TAIEX 0.001755 0.003420 0.513 0.608
L10.Copper -3.499906 7.288272 -0.480 0.631
L10.S&P 500 -0.011379 0.015556 -0.731 0.464
L10.TAIEX 0.004479 0.003404 1.316 0.188
L11.Copper 21.213781 7.252876 2.925 0.003
L11.S&P 500 0.008159 0.015229 0.536 0.592
L11.TAIEX -0.008788 0.003080 -2.853 0.004
==============================================================================
Results for equation TAIEX
==============================================================================
coefficient std. error t-stat prob
------------------------------------------------------------------------------
const 0.819865 1.431377 0.573 0.567
L1.Copper 178.778808 29.606066 6.039 0.000
L1.S&P 500 1.796227 0.057365 31.312 0.000
L1.TAIEX -0.100701 0.013842 -7.275 0.000
L2.Copper 47.365433 29.841192 1.587 0.112
L2.S&P 500 0.451291 0.063173 7.144 0.000
L2.TAIEX -0.063990 0.013911 -4.600 0.000
L3.Copper -23.989007 29.830003 -0.804 0.421
L3.S&P 500 0.245347 0.063370 3.872 0.000
L3.TAIEX 0.022098 0.013956 1.583 0.113
L4.Copper 25.907079 29.831741 0.868 0.385
L4.S&P 500 -0.033513 0.063500 -0.528 0.598
L4.TAIEX -0.047384 0.013955 -3.396 0.001
L5.Copper 26.332188 29.822893 0.883 0.377
L5.S&P 500 0.296656 0.063471 4.674 0.000
L5.TAIEX -0.035311 0.014028 -2.517 0.012
L6.Copper 3.567729 29.837764 0.120 0.905
L6.S&P 500 -0.001264 0.063476 -0.020 0.984
L6.TAIEX -0.019490 0.014043 -1.388 0.165
L7.Copper 37.377408 29.844264 1.252 0.210
L7.S&P 500 0.177728 0.063527 2.798 0.005
L7.TAIEX -0.004193 0.014014 -0.299 0.765
L8.Copper 16.852569 29.851778 0.565 0.572
L8.S&P 500 -0.011868 0.063504 -0.187 0.852
L8.TAIEX 0.021195 0.014013 1.513 0.130
L9.Copper -26.427210 29.830188 -0.886 0.376
L9.S&P 500 0.046643 0.063521 0.734 0.463
L9.TAIEX 0.019363 0.013991 1.384 0.166
L10.Copper -22.735512 29.817596 -0.762 0.446
L10.S&P 500 -0.068709 0.063642 -1.080 0.280
L10.TAIEX -0.017838 0.013926 -1.281 0.200
L11.Copper -51.761659 29.672786 -1.744 0.081
L11.S&P 500 0.173480 0.062305 2.784 0.005
L11.TAIEX -0.017929 0.012601 -1.423 0.155
==============================================================================
Correlation matrix of residuals
Copper S&P 500 TAIEX
Copper 1.000000 0.237891 0.179215
S&P 500 0.237891 1.000000 0.248966
TAIEX 0.179215 0.248966 1.000000
Granger Causality Test: S&P 500 to TAIEX
Granger Causality
number of lags (no zero) 1
ssr based F test: F=0.5134 , p=0.4737 , df_denom=5684, df_num=1
ssr based chi2 test: chi2=0.5137 , p=0.4735 , df=1
likelihood ratio test: chi2=0.5137 , p=0.4735 , df=1
parameter F test: F=0.5134 , p=0.4737 , df_denom=5684, df_num=1
Granger Causality
number of lags (no zero) 2
ssr based F test: F=0.4526 , p=0.6360 , df_denom=5681, df_num=2
ssr based chi2 test: chi2=0.9060 , p=0.6357 , df=2
likelihood ratio test: chi2=0.9059 , p=0.6358 , df=2
parameter F test: F=0.4526 , p=0.6360 , df_denom=5681, df_num=2
Granger Causality
number of lags (no zero) 3
ssr based F test: F=0.8440 , p=0.4696 , df_denom=5678, df_num=3
ssr based chi2 test: chi2=2.5351 , p=0.4690 , df=3
likelihood ratio test: chi2=2.5345 , p=0.4691 , df=3
parameter F test: F=0.8440 , p=0.4696 , df_denom=5678, df_num=3
Granger Causality
number of lags (no zero) 4
ssr based F test: F=0.7840 , p=0.5354 , df_denom=5675, df_num=4
ssr based chi2 test: chi2=3.1412 , p=0.5345 , df=4
likelihood ratio test: chi2=3.1403 , p=0.5346 , df=4
parameter F test: F=0.7840 , p=0.5354 , df_denom=5675, df_num=4
Granger Causality
number of lags (no zero) 5
ssr based F test: F=0.3779 , p=0.8642 , df_denom=5672, df_num=5
ssr based chi2 test: chi2=1.8929 , p=0.8638 , df=5
likelihood ratio test: chi2=1.8926 , p=0.8638 , df=5
parameter F test: F=0.3779 , p=0.8642 , df_denom=5672, df_num=5
Granger Causality
number of lags (no zero) 6
ssr based F test: F=0.6990 , p=0.6504 , df_denom=5669, df_num=6
ssr based chi2 test: chi2=4.2037 , p=0.6491 , df=6
likelihood ratio test: chi2=4.2022 , p=0.6493 , df=6
parameter F test: F=0.6990 , p=0.6504 , df_denom=5669, df_num=6
Granger Causality
number of lags (no zero) 7
/usr/local/lib/python3.10/dist-packages/statsmodels/tsa/stattools.py:1545: FutureWarning: verbose is deprecated since functions should not print results
warnings.warn(
ssr based F test: F=0.2182 , p=0.9813 , df_denom=5666, df_num=7
ssr based chi2 test: chi2=1.5316 , p=0.9812 , df=7
likelihood ratio test: chi2=1.5313 , p=0.9812 , df=7
parameter F test: F=0.2182 , p=0.9813 , df_denom=5666, df_num=7
Granger Causality
number of lags (no zero) 8
ssr based F test: F=0.3692 , p=0.9372 , df_denom=5663, df_num=8
ssr based chi2 test: chi2=2.9623 , p=0.9367 , df=8
likelihood ratio test: chi2=2.9615 , p=0.9367 , df=8
parameter F test: F=0.3692 , p=0.9372 , df_denom=5663, df_num=8
Granger Causality
number of lags (no zero) 9
ssr based F test: F=1.2915 , p=0.2357 , df_denom=5660, df_num=9
ssr based chi2 test: chi2=11.6627 , p=0.2330 , df=9
likelihood ratio test: chi2=11.6507 , p=0.2337 , df=9
parameter F test: F=1.2915 , p=0.2357 , df_denom=5660, df_num=9
Granger Causality
number of lags (no zero) 10
ssr based F test: F=1.5948 , p=0.1014 , df_denom=5657, df_num=10
ssr based chi2 test: chi2=16.0075 , p=0.0994 , df=10
likelihood ratio test: chi2=15.9849 , p=0.1001 , df=10
parameter F test: F=1.5948 , p=0.1014 , df_denom=5657, df_num=10
Granger Causality
number of lags (no zero) 11
ssr based F test: F=1.8886 , p=0.0360 , df_denom=5654, df_num=11
ssr based chi2 test: chi2=20.8594 , p=0.0349 , df=11
likelihood ratio test: chi2=20.8212 , p=0.0353 , df=11
parameter F test: F=1.8886 , p=0.0360 , df_denom=5654, df_num=11
Granger Causality Test: Copper to TAIEX
Granger Causality
number of lags (no zero) 1
ssr based F test: F=3.9918 , p=0.0458 , df_denom=5684, df_num=1
ssr based chi2 test: chi2=3.9939 , p=0.0457 , df=1
likelihood ratio test: chi2=3.9925 , p=0.0457 , df=1
parameter F test: F=3.9918 , p=0.0458 , df_denom=5684, df_num=1
Granger Causality
number of lags (no zero) 2
/usr/local/lib/python3.10/dist-packages/statsmodels/tsa/stattools.py:1545: FutureWarning: verbose is deprecated since functions should not print results
warnings.warn(
ssr based F test: F=4.7917 , p=0.0083 , df_denom=5681, df_num=2
ssr based chi2 test: chi2=9.5918 , p=0.0083 , df=2
likelihood ratio test: chi2=9.5837 , p=0.0083 , df=2
parameter F test: F=4.7917 , p=0.0083 , df_denom=5681, df_num=2
Granger Causality
number of lags (no zero) 3
ssr based F test: F=3.8960 , p=0.0086 , df_denom=5678, df_num=3
ssr based chi2 test: chi2=11.7025 , p=0.0085 , df=3
likelihood ratio test: chi2=11.6905 , p=0.0085 , df=3
parameter F test: F=3.8960 , p=0.0086 , df_denom=5678, df_num=3
Granger Causality
number of lags (no zero) 4
ssr based F test: F=2.8198 , p=0.0237 , df_denom=5675, df_num=4
ssr based chi2 test: chi2=11.2970 , p=0.0234 , df=4
likelihood ratio test: chi2=11.2858 , p=0.0235 , df=4
parameter F test: F=2.8198 , p=0.0237 , df_denom=5675, df_num=4
Granger Causality
number of lags (no zero) 5
ssr based F test: F=2.3116 , p=0.0415 , df_denom=5672, df_num=5
ssr based chi2 test: chi2=11.5806 , p=0.0410 , df=5
likelihood ratio test: chi2=11.5688 , p=0.0412 , df=5
parameter F test: F=2.3116 , p=0.0415 , df_denom=5672, df_num=5
Granger Causality
number of lags (no zero) 6
ssr based F test: F=2.2235 , p=0.0381 , df_denom=5669, df_num=6
ssr based chi2 test: chi2=13.3717 , p=0.0375 , df=6
likelihood ratio test: chi2=13.3560 , p=0.0377 , df=6
parameter F test: F=2.2235 , p=0.0381 , df_denom=5669, df_num=6
Granger Causality
number of lags (no zero) 7
ssr based F test: F=2.6737 , p=0.0092 , df_denom=5666, df_num=7
ssr based chi2 test: chi2=18.7656 , p=0.0090 , df=7
likelihood ratio test: chi2=18.7347 , p=0.0091 , df=7
parameter F test: F=2.6737 , p=0.0092 , df_denom=5666, df_num=7
Granger Causality
number of lags (no zero) 8
ssr based F test: F=2.3035 , p=0.0184 , df_denom=5663, df_num=8
ssr based chi2 test: chi2=18.4836 , p=0.0179 , df=8
likelihood ratio test: chi2=18.4536 , p=0.0181 , df=8
parameter F test: F=2.3035 , p=0.0184 , df_denom=5663, df_num=8
Granger Causality
number of lags (no zero) 9
ssr based F test: F=2.2420 , p=0.0170 , df_denom=5660, df_num=9
ssr based chi2 test: chi2=20.2458 , p=0.0165 , df=9
likelihood ratio test: chi2=20.2098 , p=0.0167 , df=9
parameter F test: F=2.2420 , p=0.0170 , df_denom=5660, df_num=9
Granger Causality
number of lags (no zero) 10
ssr based F test: F=2.1764 , p=0.0165 , df_denom=5657, df_num=10
ssr based chi2 test: chi2=21.8450 , p=0.0159 , df=10
likelihood ratio test: chi2=21.8031 , p=0.0161 , df=10
parameter F test: F=2.1764 , p=0.0165 , df_denom=5657, df_num=10
Granger Causality
number of lags (no zero) 11
ssr based F test: F=2.0375 , p=0.0216 , df_denom=5654, df_num=11
ssr based chi2 test: chi2=22.5033 , p=0.0208 , df=11
likelihood ratio test: chi2=22.4588 , p=0.0211 , df=11
parameter F test: F=2.0375 , p=0.0216 , df_denom=5654, df_num=11