Multivariate GARCH (MV=EWMA)

[mike80]

I tried to use the EWMA option for multivariate GARCH models. When I understand it correctly, it bases upon the exponential weighted moving average model from risk metrics. If it so, I have problems with the interpretation of the output. I get an “alpha” variable. Usually, the decay parameter is predetermined in the risk metrics model. Here, it seems to be estimated. Is it correct that the EWMA option describes a multivariate integrated GARCH with “alphas” (decay parameters) being the same for each conditional covariance and variance equation and in which the unconditional variance-covariance matrix is restricted to zero? Thanks in advance.

[TomDoan]

The EWMA has H(t)=(1-alpha)*H(t-1)+alpha*e(t-1)e(t-1)' so each element of the covariance matrix is a weighted average of its lag and the appropriate component of the other product of the lagged residual.

You're correct that you can't control the alpha when you use the GARCH instruction. However, it's a relatively simple coding to use MAXIMIZE. If you take the general setup for use of MAXIMIZE from the end of the GARCHMV.PRG example, the EWMA is done with:

Code: Select all

compute alpha=0.05
nonlin(parmset=garchparms) alpha
frml hf = (1-alpha)*h{1}+alpha*uu{1}
maximize(parmset=meanparms+garchparms,pmethod=simplex,piters=10,method=bfgs,iters=400) logl gstart gend

To estimate this with a fixed value of alpha, all you have to do is pull the <<garchparms>> out of the parmset=... That will give you the "MVGARCH" estimates for the means of the processes and the sequence of variances.