Long term covariance for Multivariate GARCH

[mengqi]

Hi,
Is there any code for calculating long term covariance matrix for multivariate GARCH-BEKK model?
Many thanks.

[mengqi]

Am I correct that for BEKK, the long run covariance matrix is equal to [(I-AA'-BB')^(-1)]*CC'
I have a bivariate-GARCH(1,1)-BEKK model, How do i generate this "I" - identity covariance matrix?
Can I use SUMMARIZE command to evaluate the long run covariance matrix?
Thanks.

[TomDoan]

Hi,
Is there any code for calculating long term covariance matrix for multivariate GARCH-BEKK model?
Many thanks.

It's easiest to do that by transforming to a VECH representation. After estimating the BEKK model:

@mvgarchtovech(mv=bekk)
*
* Check the roots of the VECH recursion
*
eigen(cvalues=cv) %%vech_a+%%vech_b
disp %cabs(cv(1))
*
* If the dominant root is larger than one, the following calculation is invalid
*
compute vechhinf=inv(%identity(%nvar*(%nvar+1)/2)-%%vech_a-%%vech_b)*%%vech_c
compute hinf=%vectosymm(vechhinf,%nvar)

[TomDoan]

Am I correct that for BEKK, the long run covariance matrix is equal to [(I-AA'-BB')^(-1)]*CC'
I have a bivariate-GARCH(1,1)-BEKK model, How do i generate this "I" - identity covariance matrix?
Can I use SUMMARIZE command to evaluate the long run covariance matrix?
Thanks.

No. You need Kroneker products for the A and B. That's why it makes more sense to convert to the VECH representation which takes care of doing the Kroneker product and reducing the calculation to the VECH of the symmetric matrix.

[mengqi]

Thanks for your reply.
I used the code but have the following results. How do i define vech_a?

eigen(cvalues=cv) %%vech_a+%%vech_b
## SX11. Identifier %%VECH_A is Not Recognizable. Incorrect Option Field or Parameter Order?
>>>>lues=cv) %%vech_a+%<<<<
If the name isn't mistyped, it's possible that you have a poorly formatted instruction
Common errors are
* a space before the ( in an option field
* a missing space before = in a SET or FRML
* a missing $ at the end of a long line which continues to the next

Many thanks.

[TomDoan]

You didn't do the @MVGARCHToVECH.

[mengqi]

Thanks. It worked. But the result is 1.10285 larger than one. So I cannot use the rest of the code?
Does it mean i cannot obtain long run covaraince?

[TomDoan]

Correct. There is no stationary solution.

[mengqi]

Dear Tom,

Can I use the above code to evaluate the long run covariance for DCC model instead of BEKK?

Regards

[TomDoan]

There is no long-run covariance for a DCC. The whole point is for the covariances to change from period to period.