[R-SIG-Finance] Garch fitting with mean regressors

Patrick Burns patrick at burns-stat.com
Wed Apr 16 17:47:50 CEST 2008

Zeno Adams wrote:
> On Wed, 16 Apr 2008 10:11:27 +0100
>  Patrick Burns <patrick at burns-stat.com> wrote:
>> You can do the regression on the returns and
>> then fit the garch model on the residuals.  That
>> will most probably be very close to the result
>> if you did it "right".
> I wonder if you could really do that. After all you would do an
> estimation ignoring heteroscedasticity in the returns which biases the
> parameter estimates. If you include the exogenous in the mean equation
> of a garch model then you take conditional heteroscedasticity into
> account. This is easy to do in most commercial software (e.g. EViews,
> RATS etc.)
> Zeno

Of course we can really do that.  The question is
whether or not it is a good idea to do it.

Yes, we are ignoring heteroscedasticity in the regression.
This makes it inefficient, but bias should be minimal.  There
is also the option to iterate the two stages which, under
suitable conditions, will converge to the maximum likelihood

If we are worried about violating assumptions, then the two
stage estimation is likely to be one of our lesser sins in the



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