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Are the test statistics and p-values viable in a regular GARCH(1,1) model where the error term is specified as GED? Both with regards to the mean equation and variance equation.

The output says "z statistic" which leads me to be in doubt as to whether inference is only reliable with normality? The help file doesn't help much in this regard.

As this is a standard maximum likelihood problem, the coefficients are asymptotically normal.

Alright. I have a large dataset, so asymptotics does seem valid. Thanks.

I have a follow up question then. If the inference is done with asymptotic normal in any case, what is the effect of choosing error distributions? My data is very fat tailed, so GED does seem appropriate, however how does that affect the model then? I do realize the ll maximizer have a different likelihood function to optimize, but I'm thinking more conceptually? Specifying one error term, and then evaluating significance with asymptotic normal?

The former is the distribution of the data generating process, the latter is the distribution of the coefficient estimates based on a maximum likelihood estimator that assumes a distribution for the data.

I have a similar question. Maybe you can help.

I'm trying to model a return series that has extremely fat tails and ARCH effects. I've tried estimating GARCH(1,1) models which does help and reduces the kurtosis and takes care of the ARCH effects.

My issue is, that I'm worried whether the model is well specified. I can use either Normal, T dist or GED distributed errors, but in any case I get a kurtosis of the standardized residuals of around 9. Do you have any suggestions as to how I can proceed? I read that the coefficient estimates should be unbiased in any case, however my estimates do difer quite a bit.

Using a normal dsitribution I can effectively use Quasi-ML and consistent standard errors, so is this optiamal? Or would a GED error specification be better to rely on the z-statistics? Or are any of them even valid?

It is hard to say without seeing the model and the workfile, but Student's t error distribution should be able to capture such a high kurtosis.