Hi Tom,
Many thanks for your kind interest in providing guidance on the queiries.
Browsing the literature reveals two different approaches in picking between symmetric and asymmetric models, say BEKK model. Some papers model both symmetric and asymmetric ones and make their decision basen on an information criteria, mostly selecting the one with the least aic value. Some others firstly model the asymmetric bekk, then apply "exclusion restrictions" type of regression test, with the null hypothesis of all D's are equal to zero. When the null is rejected, they assume that the proper model should be the asymmetric one. But, it seems that the null tends to be rejected for most of the cases.
Particularly, if the univariate garch models are GARCH(1,1), should we direcly perform symmetric bekk, or behave as those depicted above? Or, is there any other rule (or of thumb) that helps in the decision in selecting between symetric and asymmertric bekk models?
when to prefer asymmetric bekk over symmetric one...
Re: when to prefer asymmetric bekk over symmetric one...
With 4 restrictions on a 2 variable BEKK, AIC and a Wald test or likelihood ratio test will generally give very similar decisions. (The AIC penalty is 8 and the .05 critical value for the chi-square is 9.48). If you're talking about published papers, there will be a selection bias in favor of the more complicated model---if there is no apparent asymmetry, the authors may never even mention it.
Note that asymmetry in a BEKK depends upon the sign convention---because the asymmetric term can only add variance, not subtract it (since the term is positive semi-definite by construction) you get different results for a plus shock asymmetry than a minus shock asymmetry. The usual assumption is that negative shocks add variance, but that's based upon the variables being asset price returns. If one of your variables is volume, one would think that positive shocks would tend to add variance, rather than negative shocks. GARCH has a SIGNS option to control the sign which enters the asymmetry.
Note that asymmetry in a BEKK depends upon the sign convention---because the asymmetric term can only add variance, not subtract it (since the term is positive semi-definite by construction) you get different results for a plus shock asymmetry than a minus shock asymmetry. The usual assumption is that negative shocks add variance, but that's based upon the variables being asset price returns. If one of your variables is volume, one would think that positive shocks would tend to add variance, rather than negative shocks. GARCH has a SIGNS option to control the sign which enters the asymmetry.
Re: when to prefer asymmetric bekk over symmetric one...
Hi Tom,
Thanks for your reply.
I think SIGNS option in GARCH allows us to determine the sign ex ante. That is, it seems that we do not learn the sign in the output.
As for D coefficients, I think that we can only say which ones are significant, and which ones are not. We can not make any comment as to the strength of the asymmetric effect based on the size of the D coefficients, can't we?
Thanks for your reply.
I think SIGNS option in GARCH allows us to determine the sign ex ante. That is, it seems that we do not learn the sign in the output.
As for D coefficients, I think that we can only say which ones are significant, and which ones are not. We can not make any comment as to the strength of the asymmetric effect based on the size of the D coefficients, can't we?
Re: when to prefer asymmetric bekk over symmetric one...
Correct. You have to decide ahead of time which sign to use. This is not true with (for instance) GJR in a univariate model.kula wrote:Hi Tom,
Thanks for your reply.
I think SIGNS option in GARCH allows us to determine the sign ex ante. That is, it seems that we do not learn the sign in the output.
Yes, that would be the same as with the B coefficients.kula wrote: As for D coefficients, I think that we can only say which ones are significant, and which ones are not. We can not make any comment as to the strength of the asymmetric effect based on the size of the D coefficients, can't we?
I don't think I've ever seen a good justification for how the ABEKK is set up other than the fact that (a) it's asymmetric and (b) it doesn't change the forced positive definiteness of the covariance matrix. The fact that it's sign-sensitive and the interaction term is zero unless both residuals have the "correct" sign are, in my opinion, rather serious drawbacks which are generally ignored.