Non-gaussian (L-stable) Garch innovations

You are wrong
For example, a stable Gaussian GARCH(1,1) model is strictly stationary and
admits an unconditional variance that is constant (e.g. the 2nd moment of
the unconditional distribution exists and is finite). However, the
conditional variance (var(r(t)|I(t-1)) is time varying. 

-----Original Message-----
From: r-sig-finance-bounces at stat.math.ethz.ch
[mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Jos? Augusto
M. de Andrade Junior
Sent: Monday, December 24, 2007 11:27 AM
To: Patrick Burns
Cc: r-sig-finance at stat.math.ethz.ch
Subject: Re: [R-SIG-Finance] 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>:

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
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")

Josi 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.

Josi Augusto M de Andrade Jr

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