GARCH模型的参数

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

Variable Coefficient Std. Error z-Statistic Prob.

Variance Equation

C 1.31E-06 4.16E-07 3.143369 0.0017

RESID(-1)^2 0.058956 0.006407 9.202413 0.0000

GARCH(-1) 0.933369 0.007214 129.3757 0.0000

R-squared -0.001087 Mean dependent var 0.000421

Adjusted R-squared -0.000267 S.D. dependent var 0.012759

S.E. of regression 0.012760 Akaike info criterion -6.110837

Sum squared resid 0.198649 Schwarz criterion -6.098279

Log likelihood 3730.610 Hannan-Quinn criter. -6.106110

Durbin-Watson stat 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

Obs*R-squared 1.629342 Prob. Chi-Square(1) 0.2018

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 Coefficient Std. Error z-Statistic Prob.

Variance Equation

C 7.87E-07 3.87E-07 2.036199 0.0417

RESID(-1)^2 0.033905 0.013922 2.435428 0.0149

GARCH(-1) 1.475568 0.217302 6.790405 0.0000

GARCH(-2) -0.513771 0.202024 -2.543124 0.0110

R-squared -0.001087 Mean dependent var 0.000421

Adjusted R-squared -0.000267 S.D. dependent var 0.012759

S.E. of regression 0.012760 Akaike info criterion -6.113214

Sum squared resid 0.198649 Schwarz criterion -6.096471

Durbin-Watson stat 2.092936

GARCH（2,1）模型

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

Variable Coefficient Std. Error z-Statistic Prob.

Variance Equation

C 1.67E-06 5.31E-07 3.144096 0.0017

RESID(-1)^2 0.003769 0.016918 0.222791 0.8237 RESID(-2)^2 0.073854 0.019268 3.832891 0.0001 GARCH(-1) 0.913957 0.009554 95.65841 0.0000

R-squared -0.001087 Mean dependent var 0.000421 Adjusted R-squared -0.000267 S.D. dependent var 0.012759 S.E. of regression 0.012760 Akaike info criterion -6.115724 Sum squared resid 0.198649 Schwarz criterion -6.098981 Log likelihood 3734.592 Hannan-Quinn criter. -6.109422 Durbin-Watson stat 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 Coefficient Std. Error z-Statistic Prob.

Variance Equation

C(1) -0.200650 0.036753 -5.459342 0.0000

C(2) 0.142225 0.013395 10.61768 0.0000

C(3) 0.007551 0.008685 0.869409 0.3846

C(4) 0.989424 0.003546 279.0422 0.0000

R-squared -0.001087 Mean dependent var 0.000421 Adjusted R-squared -0.000267 S.D. dependent var 0.012759 S.E. of regression 0.012760 Akaike info criterion -6.115349 Sum squared resid 0.198649 Schwarz criterion -6.098606

Durbin-Watson stat 2.092936

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 Coefficient Std. Error z-Statistic Prob.

@SQRT(GARCH) 0.046034 0.029263 1.573117 0.1157

Variance Equation

C(2) -0.196146 0.036315 -5.401162 0.0000

C(3) 0.141295 0.013095 10.78965 0.0000

C(4) 0.011524 0.008976 1.283855 0.1992

C(5) 0.989787 0.003510 281.9926 0.0000

R-squared -0.001415 Mean dependent var 0.000421 Adjusted R-squared -0.001415 S.D. dependent var 0.012759 S.E. of regression 0.012768 Akaike info criterion -6.116227 Sum squared resid 0.198714 Schwarz criterion -6.095298 Log likelihood 3735.898 Hannan-Quinn criter. -6.108350 Durbin-Watson stat 2.092126