Hi Patrick,

Thanks for the explanation.

I want to discuss the infinite variance of stable distributions (except
normal). I understand that infinite variance means only that this
distributions does not have a constant variance, that the integral does not
converge to a finite constant value.

When someone uses GARCH to model the variance he is indeed recogning the
same fact: the varince is not constant and should not converge, as with
stable distributions also occur.

Am i wrong?

2007/12/24, Patrick Burns <patrick@burns-stat.com>:
>
> Given the model parameters and the starting volatility state,
> the procedure (which you can use a 'for' loop to do) is:
>
> * select the next random innovation.
>
> * multiply by the volatility at that time point to get the simulated
> return for that period.
>
> * use the return to get the next period's variance using the garch
> equation.
>
> So there are two series that are being produced: the return
> series and the variance series.
>
>
> I'm not exactly objecting, but I hope you realize that garch models
> variances while stable distributions (except the Gaussian) have infinite
> variance.  Hence a garch model with a stable distribution is at least
> a bit nonsensical.
>
> Patrick Burns
> patrick@burns-stat.com
> +44 (0)20 8525 0696
> http://www.burns-stat.com
> (home of S Poetry and "A Guide for the Unwilling S User")
>
> José Augusto M. de Andrade Junior wrote:
>
> >Hi,
> >
> >Could someone give an example on how to simulate paths (forecast) of a
> Garch
> >process with Levy stable innovations (by using rstable random deviates,
> for
> >example)?
> >
> >Thanks in advance.
> >
> >José Augusto M de Andrade Jr
> >
> >       [[alternative HTML version deleted]]
> >
> >
> >
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