Thanks to anyone who replied to my question from a week ago.
Seems as if GARCH models currently can not be estimated with winbugs.
In the following I paste some of the replies I received.
Stephan
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From: David Spiegelhalter <[log in to unmask]>
I think that it's because the GARCH model only has 4 unknown parameters,
but sampling each is extremely difficult and time-consuming due to their
complex likelihoods. The volatility model has much more flexibility,
more parameters but each simpler to sample. WinBUGS is not slowed down
so much by having loads of things to sample, it is slowed by having very
long expressions to calculate when sampling each element.
Also WinBUGS was designed mainly for 'vertical' hierarchical models in
which single-element updating is fairly efficient, and not for 'flat'
GARCH-type models for which it is likely to be very inefficient. Sorry
about this - WinBUGS grew out of biostatistics!
I hope this makes sense.
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From: "Pablo Verde" <...>
Some points in your parametrization:
1) The unconditional variance of your GARCH(1,1) can be negative!
Var(y)=mu/(1-alpha-beta). You need to make constrains to these parameter
values.
mu > 0 and alpha+beta < 1. These constrains also assure stationarity.
2) For a GARC(1,0) a possible solution (I didnt try it) is:
mu ~ U(0,1000)
alpha ~U(0,1)
3) The stochastic nodes power(y[t-1],2) are autocorrelated.
This issue make convergence difficult.
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From: millar <...>
I've come across that before - the full conditionals are easier for
BUGS to sample from in the stochastic model, because it is able to
condition on the state at each time point.
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