关于garch模型
1、什么是garch效应??
ARCH Test:
F-statistic 0.0364991883278443 Probability 0.848490453059744
Obs*R-squared 0.0365031766428946 Probability 0.848480117146432
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 09/15/10 Time: 09:53
Sample (adjusted): 3 17973
Included observations: 17971 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 0.00029866993760912 3.72861456738888e-05 8.01021216355638 1.21459502500532e-15
RESID^2(-1) 0.00142521107019859 0.00745997866346969 0.191047606768317 0.848490453564656
R-squared 2.03122678998913e-06 Mean dependent var 0.000299096206807761
Adjusted R-squared -5.36200598022507e-05 S.D. dependent var 0.00498933881923096
S.E. of regression 0.00498947258176083 Akaike info criterion -7.76286178905703
Sum squared resid 0.447335319658607 Schwarz criterion -7.7619941117295
Log likelihood 69755.1946055719 F-statistic 0.0364991883278443
Durbin-Watson stat 2.00000296865432 Prob(F-statistic) 0.848490453059744
从这个结果看,是不是没有garch效应阿??
3、如果结果向上面所示的话,是不是不能采用garch和arch模型描述序列??
4、如果强行进行arch估计的话,我可以得到以下结果,这个结果是不是不能采用?
Dependent Variable: RT
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 09/15/10 Time: 09:57
Sample (adjusted): 2 17973
Included observations: 17972 after adjustments
Convergence achieved after 67 iterations
Variance backcast: ON
GARCH = C(2) + C(3)*RESID(-1)^2 + C(4)*RESID(-2)^2 + C(5)*RESID(
-3)^2 + C(6)*RESID(-4)^2 + C(7)*RESID(-5)^2
Coefficient Std. Error z-Statistic Prob.
C -0.000487 3.16E-05 -15.42420 0.0000
Variance Equation
C 0.000127 2.82E-07 449.4298 0.0000
RESID(-1)^2 0.065632 0.002688 24.41336 0.0000
RESID(-2)^2 0.652273 0.003513 185.6740 0.0000
RESID(-3)^2 0.003343 0.000715 4.675561 0.0000
RESID(-4)^2 0.131957 0.001492 88.42223 0.0000
RESID(-5)^2 0.306702 0.002549 120.3201 0.0000
R-squared -0.000865 Mean dependent var 2.17E-05
Adjusted R-squared -0.001200 S.D. dependent var 0.017294
S.E. of regression 0.017305 Akaike info criterion -5.465051
Sum squared resid 5.379709 Schwarz criterion -5.462015
Log likelihood 49115.95 Durbin-Watson stat 2.074734
5、如果进行garch模型的话,所得的结果如下,不知道可否使用??
Dependent Variable: RT
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 09/15/10 Time: 09:59
Sample (adjusted): 2 17973
Included observations: 17972 after adjustments
Convergence achieved after 29 iterations
Variance backcast: ON
GARCH = C(2) + C(3)*RESID(-1)^2 + C(4)*GARCH(-1)
Coefficient Std. Error z-Statistic Prob.
C -0.000224 3.78E-05 -5.909177 0.0000
Variance Equation
C 4.99E-05 2.08E-07 239.7977 0.0000
RESID(-1)^2 0.367496 0.001701 216.0826 0.0000
GARCH(-1) 0.636541 0.001220 521.5446 0.0000
R-squared -0.000201 Mean dependent var 2.17E-05
Adjusted R-squared -0.000368 S.D. dependent var 0.017294
S.E. of regression 0.017298 Akaike info criterion -5.417299
Sum squared resid 5.376140 Schwarz criterion -5.415564
Log likelihood 48683.85 Durbin-Watson stat 2.076111
6、tarch模型的结果如下
Dependent Variable: RT
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 09/15/10 Time: 10:01
Sample (adjusted): 2 17973
Included observations: 17972 after adjustments
Convergence achieved after 16 iterations
Variance backcast: ON
GARCH = C(2) + C(3)*RESID(-1)^2 + C(4)*RESID(-1)^2*(RESID(-1)<0)
+ C(5)*GARCH(-1)
Coefficient Std. Error z-Statistic Prob.
C 2.49E-05 0.000150 0.165680 0.8684
Variance Equation
C 0.000150 1.40E-06 107.0805 0.0000
RESID(-1)^2 0.425548 0.007178 59.28574 0.0000
RESID(-1)^2*(RESID(-1)<0) -0.427103 0.007167 -59.59612 0.0000
GARCH(-1) 0.575350 0.003551 162.0410 0.0000
R-squared -0.000000 Mean dependent var 2.17E-05
Adjusted R-squared -0.000223 S.D. dependent var 0.017294
S.E. of regression 0.017296 Akaike info criterion -5.283955
Sum squared resid 5.375058 Schwarz criterion -5.281786
Log likelihood 47486.62 Durbin-Watson stat 2.076529
7、Egarch的模型结果
Dependent Variable: RT
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 09/15/10 Time: 10:03
Sample (adjusted): 2 17973
Included observations: 17972 after adjustments
Convergence achieved after 45 iterations
Variance backcast: ON
LOG(GARCH) = C(2) + C(3)*ABS(RESID(-1)/@SQRT(GARCH(-1))) +
C(4)*RESID(-1)/@SQRT(GARCH(-1)) + C(5)*LOG(GARCH(-1))
Coefficient Std. Error z-Statistic Prob.
C 0.000749 3.33E-05 22.49011 0.0000
Variance Equation
C(2) -1.192200 0.005455 -218.5360 0.0000
C(3) 0.304854 0.001069 285.2963 0.0000
C(4) 0.147385 0.001411 104.4881 0.0000
C(5) 0.873973 0.000618 1414.113 0.0000
R-squared -0.001770 Mean dependent var 2.17E-05
Adjusted R-squared -0.001993 S.D. dependent var 0.017294
S.E. of regression 0.017312 Akaike info criterion -5.411697
Sum squared resid 5.384572 Schwarz criterion -5.409528
Log likelihood 48634.51 Durbin-Watson stat 2.072860
请教各位老师,请问以上的步骤是可行的吗??由于最初的残差检验出不存在garch效应,但是为什么后面的结果都还比较显著呢??谢谢