Hi Tom,
I have estimated a GARCH BEKK model and the model did not pass some diagnostic tests. However, when I estimated the VECH version of the model, the model passed all the diagnostic tests. My only concern is that as it is stated in the notes, the VECH model does not guarantee positive definiteness. Therefore, I am not sure whether it is appropriate to use the model if it is good enough to use of the intended purpose. If so, how do I justify the use of the model since the VECH does not guarantee positive definiteness.
Thank you
Using the VECH Model
Re: Using the VECH Model
A full VECH model, or a DVECH? The full VECH usually has far too many parameters to be estimated.
The advantage of the positive-definiteness of the BEKK is greatly overstated. Any multivariate GARCH model that gets estimated has positive definite covariance matrices in sample---if it didn't, the log likelihood would be -infinity. Where the forced positive-definiteness would come into play is if you simulate the model. A BEKK, by construction, will always produce a p.s.d. covariance matrix no matter what residuals are thrown at it, no matter how far-fetched, while a DVECH or VECH may have some (typically highly unlikely) sequences of residuals that may cause it to produce a non p.s.d. covariance matrix. In practice, however, that won't happen.
The advantage of the positive-definiteness of the BEKK is greatly overstated. Any multivariate GARCH model that gets estimated has positive definite covariance matrices in sample---if it didn't, the log likelihood would be -infinity. Where the forced positive-definiteness would come into play is if you simulate the model. A BEKK, by construction, will always produce a p.s.d. covariance matrix no matter what residuals are thrown at it, no matter how far-fetched, while a DVECH or VECH may have some (typically highly unlikely) sequences of residuals that may cause it to produce a non p.s.d. covariance matrix. In practice, however, that won't happen.
Re: Using the VECH Model
Thank you for the reply. I am considering a DVECH model. So is it okay for me to use the DVECH because as you stated, the problems associated with the DVCEH won't happen in practice?
Thank you
Thank you
Re: Using the VECH Model
Certainly if the DVECH seems to work better than a BEKK.
Re: Using the VECH Model
Thank you. The DVECH seems to produce the expected results and it also passes all diagnostic tests. However, the model doesn't converge even after several iterations. Do you know what I can do in order to achieve convergence of the DVECH model?
Thank you
Thank you
Re: Using the VECH Model
Are you using log returns or 100*log returns? The latter is much better numerically.
Re: Using the VECH Model
I am using log returns. Do you mean multiplying the log returns by 100 is better?
Re: Using the VECH Model
Yes. In Data Preparations and Preliminaries in the User's Guide it recommends that. It changes the scales of some of the GARCH coefficients to make it easier to estimate. (It's a numerical issue, not a statistical one).