[R-SIG-Finance] Non-gaussian (L-stable) Garch innovations

[Patrick Burns]

Yes, you are wrong.  Stable distributions DO have
a constant variance: infinity.

Pat

José Augusto M. de Andrade Junior wrote:

> 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")
>
>     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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