That is because the series returned from the GARCH simulation is not the
volatility series, it is the return series. In other words, the
volatility series needs to be extracted from the model once you've run
your simulation. To repeat: you are NOT getting negative volatilities.
You are getting negative returns, which is perfectly sensible. To
extract the volatility series, do as Martin suggested and you ought to
be fine.

On Wed, 2010-01-27 at 14:28 +0100, Trafim Vanishek wrote:

> Thanks for the answer.
> But it is following from the definition of GARCH model:
> sigma_t^2=a0+a1*epsilon_t-1^2+b1*sigma_t-1^2
> 
> therefore, with positive a0, a1, b1 it should always stay positive.
> 
> On Wed, Jan 27, 2010 at 2:19 PM, Matthias Koberstein <
> Matthias.Koberstein@hsbctrinkaus.de> wrote:
> 
> >
> > Hi,
> >
> > R does not know that you want to simulate volatility by default.
> > You can start your series with whatever values you want.
> > If you start them with the values from the code below your presample can be
> > negative and therefore many future values will be too.
> > To look at your presample try to look at the "spec" after you defined it.
> > You are likely to see some negative values.
> > I think by default they are taken from a normal distribution but I am not
> > sure on that.
> >
> > Cheers
> >
> > Matthias
> >
> >
> >
> >  Von:
> > Trafim Vanishek <rdapamoga@gmail.com>
> > An: r-sig-finance@stat.math.ethz.ch Datum: 27.01.2010 13:56 Betreff: [R-SIG-Finance]
> > GARCH (1,1) negative volatility??? Gesendet von:
> > r-sig-finance-bounces@stat.math.ethz.ch
> > ------------------------------
> >
> >
> >
> > Dear all,
> >
> > I am using GARCH (1,1) model to simulate volatility.
> > But seems that I am missing something about how it works in R.
> >
> > The following code produces negative results, though vola cannot be.
> > What is wrong here?
> >
> > library("fSeries")
> > library("fGarch")
> >
> > spec = garchSpec(model = list(omega = 0.01, alpha = 0.13, beta = 0.86))
> > gat <- garchSim(spec, n = 10)
> >
> > Thanks a lot!
> >
> >                 [[alternative HTML version deleted]]
> >
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