[R-SIG-Finance] garch vs garchFit - minimum sample size

[Achim Zeileis]

Spencer,

I'll try to answer your questions but just as a disclaimer: I'm really no
expert in GARCH estimation. Also I have just read some parts of the
garch() and garchFit() code and the authors of the respective function can
surely comment more competently on this.

>       Is it fair to say that 'garchFit' is newer

Yes.

> and uses a more general and robust algorithm?

I'm not sure here. garchFit() certainly fits a much more general model
class but the algorithms (there is not only one) it interfaces are not
as such more general, I think. It is also a bit unclear what that would
mean exactly.

As far as I can see, Diethelm and Yohan have been quite busy improving
the optimizers and also their documentation (which seems to be more
detailed in the devel-version of the package, maybe Yohan or Diethelm
can comment on this). I think (but might be wrong here) that all
optimizers used by garchFit() rely on numerical gradients and numerical
Hessians.

Adrian's code comes with its own optimzer (Quasi-Newton) which is not
available in garchFit() (I think) and provides both analytical and
numerical gradients (Gaussian conditional distribution only).

To the best of my knowledge, analytical Hessians are available in neither
function.

>       Or are there circumstances under which 'garch' would give better
> answers than 'garchFit'?

I encountered situations where the likelihood returned by garch() was
slightly larger than that by garchFit() when both converged to the same
maximum. But it's quite likely that I could have improved that by tweaking
the optimization in garchFit(). And, as you also illustrated, there are
situations where garchFit() converges while garch() does not.

In any case, as I already said in my previous post: "better" just pertains
to the coefficient estimates while the estimates for the standard
deviation are mainly "different". And I think that none of the covariance
estimators is uniformly dominated by all others.

hth,
Z