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* GARCH Model Fit *
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Conditional Variance Dynamics
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GARCH Model : eGARCH(1,1)
Mean Model : ARFIMA(0,0,0)
Distribution : std
Optimal Parameters
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Estimate Std. Error t value Pr(>|t|)
mu -0.000232 0.000097 -2.40006 0.016392
omega -0.378463 0.018650 -20.29334 0.000000
alpha1 -0.028542 0.030402 -0.93883 0.347820
beta1 0.967431 0.001671 578.86064 0.000000
gamma1 0.153617 0.034882 4.40394 0.000011
shape 13.356411 5.860378 2.27910 0.022661
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu -0.000232 0.000069 -3.33948 0.000839
omega -0.378463 0.027513 -13.75584 0.000000
alpha1 -0.028542 0.041941 -0.68053 0.496171
beta1 0.967431 0.002550 379.42164 0.000000
gamma1 0.153617 0.036893 4.16388 0.000031
shape 13.356411 6.304088 2.11869 0.034117
LogLikelihood : 2923.029
Information Criteria
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Akaike -8.7995
Bayes -8.7588
Shibata -8.7996
Hannan-Quinn -8.7837
Weighted Ljung-Box Test on Standardized Residuals
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statistic p-value
Lag[1] 0.1001 7.517e-01
Lag[2*(p+q)+(p+q)-1][2] 0.8006 5.677e-01
Lag[4*(p+q)+(p+q)-1][5] 17.4389 9.735e-05
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
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statistic p-value
Lag[1] 5.272 0.02167
Lag[2*(p+q)+(p+q)-1][5] 8.714 0.01954
Lag[4*(p+q)+(p+q)-1][9] 11.197 0.02750
d.o.f=2
Weighted ARCH LM Tests
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Statistic Shape Scale P-Value
ARCH Lag[3] 2.772 0.500 2.000 0.09593
ARCH Lag[5] 3.093 1.440 1.667 0.27653
ARCH Lag[7] 3.998 2.315 1.543 0.34690
Nyblom stability test
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Joint Statistic: 1.7516
Individual Statistics:
mu 0.28653
omega 0.28846
alpha1 0.61612
beta1 0.28047
gamma1 0.72655
shape 0.02008
Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 1.49 1.68 2.12
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
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t-value prob sig
Sign Bias 0.6346 0.52589
Negative Sign Bias 1.9883 0.04719 **
Positive Sign Bias 1.8779 0.06083 *
Joint Effect 7.9623 0.04680 **
Adjusted Pearson Goodness-of-Fit Test:
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group statistic p-value(g-1)
1 20 18.90 0.4632
2 30 28.18 0.5085
3 40 40.05 0.4235
4 50 50.65 0.4082
Elapsed time : 0.4520249