Nullity of coefficients in GARCH models

[Annini]

Hey everyone,

I am a Eviews greenhorn, but the following has not become clear to me yet:
When I estimate my model using OLS (n=355) the t-statistic is reportet for the coefficients. When I include a GARCH process for the variance of error terms the test statistic for the coeffients automatically switches to a z-statistic.
I did not find any theoretical explanation for this in the Eviews users guid and would now like to know whether anyone can explain me why this is so and possibly name give me some hint where I can find for a theoretical explanation in the literature.

Thanks in advance.

Yours, Annini

[startz]

GARCH results are only asymptotic, so the normal distribution (Z-score) is used. With n=355, there's no detectable difference anyway.

[Annini]

Hey Startz,

thank you for your reply.
I am familiar with the fact, that the distribution is assumed to converge against the normal distribution with large ns.
However, this is also the case for OLS.
So why is a t-test used for the OLS and a z-test for the GARCH model??

Maybe the answer lies in your "GARCH results are only asymptotic (...)". But I have no clue what it is supposed to mean.
It would be great if someone could extend a bit on this matter.

Thank you very much in advance!
Annini

[startz]

In OLS, if the error terms are normal then the coefficients are distributed t-. For GARCH, even if the errors are normal the distribution the distribution of the coefficients is known only approximately. In a large sample (that's what asymptotic means), the coefficients are approximately normal.

[Annini]

Hey Starz,

ah ok! That I understand some better, thank you!
Do you maybe have any literature recommendation(s) for me regarding this topic??

Cheers,
Anna

[startz]

Hey Starz,

ah ok! That I understand some better, thank you!
Do you maybe have any literature recommendation(s) for me regarding this topic??

Cheers,
Anna

Most econometrics books, except the most basic, cover this sort of stuff. Introductory Econometrics by Wooldridge is one nice one.