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Simultaneous estimation of mean and garch eq'n

3 messages · Tobias Muhlhofer, Dirk Eddelbuettel, Patrick Burns

Tobias Muhlhofer
# 
Is it possible to simultaneously estimate mean and GARCH parameters in R?

In other words, I would like to estimate the normal regression equation

Y = b X + u

and simultaneously do a garch process on the u's to correct the standard 
errors.

I was thinking maybe something with systemfit(), but I can't quite come 
up with it.

Thanks,
	Tobias
--
Dirk Eddelbuettel
# 
Tobias Muhlhofer <t.muhlhofer <at> lse.ac.uk> writes:
It is but you have to write out the loglikelihood (and possibly its gradient)
which you could then maximise with optim() and friends.  Adrian's GARCH(1,1)
is hard-coded with an analytic gradient -- the convenience of having this 
powerful routine pre-made and comes at the price of its lack of flexibility.

Diethelm's fSeries from Rmetrics can estimate Garch models by calling Ox. That
may work for you too.

Hope this helps,  Dirk
Patrick Burns
# 
It is my experience that location parameters are not very affected
by the garch parameters.  So doing a naive estimate of location,
followed by the garch estimate, followed by an estimate of location
accounting for heteroskedasticity is likely to be indistinguishable
from the estimates from the full likelihood.

If you compare garch with the naive estimate of location versus the
garch estimate with no estimate of location, you are probably not
going to see much difference.  That difference is likely to be smaller
than if you change the time period of estimation slightly.

Patrick Burns

Burns Statistics
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")
Tobias Muhlhofer wrote: