大家好,我在建立ARMA-GARCH模型的过程中,发现我单独建立ARMA模型以及在GARCH模型中建立的ARMA模型,均值方程的系数不一样,现在不太清楚原因,以及我如果要写均值方程,该按照哪个系数写呢?谢谢大佬们
如下两表,首先是单独建立ARMA模型,
Method: ARMA Maximum Likelihood (OPG - BHHH)
Date: 05/15/23 Time: 17:17
Sample: 4/16/2008 11/30/2022
Included observations: 3558
Convergence achieved after 29 iterations
Coefficient covariance computed using outer product of gradients
Variable Coefficient Std. Error t-Statistic Prob.
AR(1) -0.235791 0.178559 -1.320520 0.1867
MA(1) 0.293657 0.175044 1.677619 0.0935
SIGMASQ 0.000329 4.62E-06 71.13951 0.0000
R-squared 0.003474 Mean dependent var 0.000141
Adjusted R-squared 0.002913 S.D. dependent var 0.018166
S.E. of regression 0.018140 Akaike info criterion -5.180600
Sum squared resid 1.169749 Schwarz criterion -5.175392
Log likelihood 9219.288 Hannan-Quinn criter. -5.178743
Durbin-Watson stat 1.998059
其次是在GARCH模型中建立的ARMA模型,
Method: ML ARCH - Normal distribution (BFGS / Marquardt steps)
Date: 05/15/23 Time: 17:18
Sample (adjusted): 4/17/2008 11/30/2022
Included observations: 3557 after adjustments
Convergence achieved after 53 iterations
Coefficient covariance computed using outer product of gradients
MA Backcast: 4/16/2008
Presample variance: backcast (parameter = 0.7)
GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1) + C(6)*DV
Variable Coefficient Std. Error z-Statistic Prob.
AR(1) -0.645665 0.185259 -3.485207 0.0005
MA(1) 0.684735 0.177369 3.860503 0.0001
Variance Equation
C 4.95E-06 7.79E-07 6.351343 0.0000
RESID(-1)^2 0.064363 0.004503 14.29244 0.0000
GARCH(-1) 0.921900 0.004540 203.0803 0.0000
DV -1.66E-06 6.13E-07 -2.707713 0.0068
R-squared 0.002821 Mean dependent var 0.000148
Adjusted R-squared 0.002540 S.D. dependent var 0.018164
S.E. of regression 0.018141 Akaike info criterion -5.456757
Sum squared resid 1.169917 Schwarz criterion -5.446338
Log likelihood 9710.842 Hannan-Quinn criter. -5.453041
Durbin-Watson stat 1.959753