GARCH模型的参数

GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1)

Variable

C RESID(-1)^2 GARCH(-1)

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient

Std. Error

z-Statistic 3.143369 9.202413 129.3757

Prob. 0.0017 0.0000 0.0000 0.000421 0.012759 -6.110837 -6.098279 -6.106110

Variance Equation 1.31E-06 0.058956 0.933369

4.16E-07 0.006407 0.007214

-0.001087 Mean dependent var -0.000267 S.D. dependent var 0.012760 Akaike info criterion 0.198649 Schwarz criterion 3730.610 Hannan-Quinn criter. 2.092936

对GARCH（1,1）模型做出的LM检验，发现F统计量和卡方统计量都大于0.05，所以不存在ARCG效应 Heteroskedasticity Test: ARCH F-statistic

1.628845 Prob. F(1,1217)

0.2021 0.2021

Obs*R-squared

1.629342 Prob. Chi-Square(1)

下面是GARCH(1，2)和GARCH（2,1）模型阐述估计

GARCH（1,2）

GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*GARCH(-1) + C(4)*GARCH(-2)

Variable

C RESID(-1)^2 GARCH(-1) GARCH(-2)

R-squared Adjusted R-squared S.E. of regression Sum squared resid

Coefficient

Std. Error

z-Statistic 2.036199 2.435428 6.790405 -2.543124

Prob. 0.0417 0.0149 0.0000 0.0110 0.000421 0.012759 -6.113214 -6.096471

Variance Equation 7.87E-07 0.033905 1.475568 -0.513771

3.87E-07 0.013922 0.217302 0.202124

-0.001087 Mean dependent var -0.000267 S.D. dependent var 0.012760 Akaike info criterion 0.198649 Schwarz criterion

Log likelihood Durbin-Watson stat

GARCH（2,1）模型

3733.061 Hannan-Quinn criter. 2.092936

-6.106912

GARCH = C(1) + C(2)*RESID(-1)^2 + C(3)*RESID(-2)^2 + C(4)*GARCH(-1)

Variable

C RESID(-1)^2 RESID(-2)^2 GARCH(-1)

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient

Std. Error

z-Statistic 3.144096 0.222791 3.832891 95.65841

Prob. 0.0017 0.8237 0.0001 0.0000 0.000421 0.012759 -6.115724 -6.098981 -6.109422

Variance Equation 1.67E-06 0.003769 0.073854 0.913957

5.31E-07 0.016918 0.019268 0.009554

-0.001087 Mean dependent var -0.000267 S.D. dependent var 0.012760 Akaike info criterion 0.198649 Schwarz criterion 3734.592 Hannan-Quinn criter. 2.092936

EARCH模型

LOG(GARCH) = C(1) + C(2)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(3) *RESID(-1)/@SQRT(GARCH(-1)) + C(4)*LOG(GARCH(-1))

Variable

C(1) C(2) C(3) C(4)

R-squared Adjusted R-squared S.E. of regression Sum squared resid

Coefficient

Std. Error

z-Statistic -5.459342 10.61768 0.869409 279.0422

Prob. 0.0000 0.0000 0.3846 0.0000 0.000421 0.012759 -6.115349 -6.098606

Variance Equation -0.202150 0.142225 0.007551 0.989424

0.036753 0.013395 0.008685 0.003546

-0.001087 Mean dependent var -0.000267 S.D. dependent var 0.012760 Akaike info criterion 0.198649 Schwarz criterion

Log likelihood Durbin-Watson stat

3734.363 Hannan-Quinn criter. 2.092936

-6.109047

LOG(GARCH) = C(2) + C(3)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + C(4) *RESID(-1)/@SQRT(GARCH(-1)) + C(5)*LOG(GARCH(-1))

Variable @SQRT(GARCH)

C(2) C(3) C(4) C(5)

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

Coefficient 0.046034

Std. Error 0.029263

z-Statistic 1.573117 -5.401162 10.78965 1.283855 281.9926

Prob. 0.1157 0.0000 0.0000 0.1992 0.0000 0.000421 0.012759 -6.116227 -6.095298 -6.108350

Variance Equation -0.196146 0.141295 0.011524 0.989787

0.036315 0.013095 0.008976 0.003510

-0.001415 Mean dependent var -0.001415 S.D. dependent var 0.012768 Akaike info criterion 0.198714 Schwarz criterion 3735.898 Hannan-Quinn criter. 2.092126

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