Multivariate GARCH

[dinu]

Hi David,

I am Dinu.

I have a doubt regarding using multivariate GARCH.

If a dependant vairable for ex, share returns is assumed to be affected by more than 3 factors how do we account for these in the GARCH functional form, i.e; whether the lag of the dependant variable can also be used in the estimation process.

Iam just confused as to how the mathematical form will look like.

Looking forward to hearing from you soon.

Keep up the good work!

Regards

Dinu

 

[David Harper CFA FRM]

Hi Dinu,

It's a big topic, Carol Alexander has a good discussion in Vol II (Practical Financial Econometrics); I mention her terrific book b/c she points to the *attached* paper which will give you a taste.

You'll notice there are different sub-classes (and, for some, mGARCH suggests the incorporation of lagged covariances as the additional factors). But long story short, the Factor GARCH (page 6 + ) use MATRIX notion to capture the additional factors. But, if you string out the matrices into long-hand, it's really a generalization of our familiar GARCH(1,1) which itself is *sort of* a multi-factor model:

variance = (gamma weight * LR variance) + (beta weight * lag variance) + (alpha weight * lag return^2)

Here, alpha + beta + gamma (where gamma*LR variance = omega) = 1.0, so they are weights on the factors. In a similar way, to long hand the matrix notion is to add terms with additional weights to each factor, where ultimately the variance estimate is a sum of weighted factors...hope that's helpful, totally thanks for your kind feedback!

David

 

[dinu]

Hi David,

Thanks a lot!

It has made my thinking process a lot less complicated.

Regards

Dinu

 

[milans]

Hi David
The attached mgarch.pdf does not open. I have tried numerous times, can you please reload it.

Thanks,
Milan