Diagnostic Test for Multivariate GARCH Model

[Zankawa]

Hi Tom,
Following the version 8 user's guide, I have used the HMATRICES and RVECTORS to save the covariance matrices and the residuals because I don't have access to the version 9. I have estimated the model as
GARCH(MODEL=GARCHM,P=1,Q=1,MV=TBEKK,ASYMMETRIC,ITERS=300,PMETHOD=BFGS,PITERS=15,MVHSERIES=hhs,hmatrices=hh,rvectors=rd) / DLGSECI DLEXR DLSP500 DLCOP
However, am not sure where the covariance matrices and residuals are saved. I checked in the series window but could not find them there. I also used the MVHSERIES option but am not sure how and where the covariance matrix is provided. I also tried using the @MVQSTAT procedure but I am getting an error message in the third step of this procedure. This is the message I obtained after step 3.
compute %pt(zu,time,%solve(%decomp(hh(time)),rd(time)))
## MAT15. Subscripts Too Large or Non-Positive

Am not sure why I got this message and I wanted to ask if you give me further guidance on how I go around all these.
Thank you always

[TomDoan]

The GARCHMV.RPF program for version 8 works fine, so you must be doing something wrong. The HMATRICES option creates a SERIES[SYMM] and RVECTOR produces a SERIES[VECT]. They create full matrices because you have to manipulate them as matrices in order to do a multivariate standardization.

[Zankawa]

Thank you for the reply. You said the HMATRICES option creates a SERIES[SYMM] and RVECTOR creates a SERIES[VECT]. Do you know where in the RATS software that those series are saved? I used hmatrices=hh and rvectors=rd in my garch model but I cannot find the variance and residual series in the series window after estimating the garch model. I thought the variance and residual series might have been saved somewhere that I don't know because adding the HMATRICES and RVECTORS options in the model produces some results.

[TomDoan]

That's all described in the v8 User's Guide. You use them as described there. They won't show in the series window because they aren't standard series---they're series of matrices.

[Zankawa]

Dear Tom,
Following the version 8 user's guide, I am now able to conduct a diagnostic test for a multivariate GARCH model (with lags 17 and 24) and the procedure and results are provided below;
dec vect[series] zu(%nvar)
do time=%regstart(),%regend()
compute %pt(zu,time,%solve(%decomp(hh(time)),rd(time)))
end do time

@mvqstat(lags=17)
# zu
Multivariate Q(17)= 309.79633
Significance Level as Chi-Squared(272)= 0.05714

@mvqstat(lags=24)
# zu
Multivariate Q(24)= 469.93404
Significance Level as Chi-Squared(384)= 0.00175

Since this procedure is a multivariate generalization of the Ljung-Box Q-statistic, is it sufficient to use this test result for both the mean and variance equations of the GARCH model. In the univariate case, you test the standardized residuals for the mean equation and the squared standardized residuals for the variance equation. I am not sure if this applies to the multivariate models as well, and if so, how will this result be used to explain serial correlation in both the mean and the variance equations.

[TomDoan]

No. That's only a test for serial correlation. This is not like the univariate residuals where you can test serial correlation on the squares to test for remaining ARCH. You use @MVARCHTEST to do a multivariate test for remaining ARCH.

[Zankawa]

Thank you for the reply. So I want to get this right; In the multivariate case, the @mvqstat procedure is a test for serial correlation for the whole model(both mean and variance equations) whilst the @mvarchtest procedure is a test for ARCH presence in the model, am I right?

[TomDoan]

@MVQSTAT is a test for serial correlation in the mean model, given the variance model (which is used to standardize the residuals). It's not really testing anything specific about the variance model itself.

[Zankawa]

So in this case, how do I obtain a Ljung-Box Q-test for the variance model? or is it the case that a Q-test for the variance model is not necessary once the @mvarchtest has been conducted?
Thank you once again for your kind responses.

[TomDoan]

You don't. There's no direct generalization of the McLeod-Li test to multivariate systems.

[Zankawa]

Okay. So is it appropriate to state that if the multivariate model is adequate, the @MVQSTAT test should not be significant and the @MVARCHTest statistic should not also be significant?

[TomDoan]

Yes. Sometimes hard to do with a big enough data set, but that would be the goal.

[Zankawa]

Thank you so much for all the replies Tom. My final question is, I am working with monthly data with 300 observations and am not sure how many lags to choose in the @MVQSTAT test. Do you know if there is a guide on the appropriate number of lags to choose when testing the MVQSTAT with monthly data?
Thank you

[TomDoan]

Not a lot. Maybe 6. If there's anything fixable by adjusting the mean model, it will show up in the short lags.