Non-gaussian (L-stable) Garch innovations

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 at burns-stat.com 
<mailto:patrick at 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 at burns-stat.com <mailto:patrick at 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")

    Jos? 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.
    >
    >Jos? Augusto M de Andrade Jr
    >
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