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

[Yohan Chalabi]

>>>> "AZ" == Achim Zeileis <Achim.Zeileis at wu-wien.ac.at>
>>>> on Wed, 13 Feb 2008 22:22:58 +0100 (CET)


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

We have implemented a new optimization scheme  "mnfb" in the
devel-version of fGarch
(https://svn.r-project.org/Rmetrics/trunk/fGarch). It is actually the
same fortran library as used in the R function nlminb(). But we have
implemented the whole optimization in fortran. 

As you have noticed it, we are also working on the documentation and we
hope the new manual page is more readable.

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

In garchFit you can choose between 5 different optimizations
schemes : "nlminb" , "mnfb" (in devel-version), "sqp", "lbfgsb",
"nlminb+nm", "lbfgsb+nm". Please read the man page for more details. 

Although the analytical gradient and hessian of ARMA-APARCH for
Gaussian conditional distribution can be  calculated without too
much of effort, the analytical solutions for other
distribution are not trivial. Since garchFit can handle different 
conditional distributions ("norm", "snorm", "ged", "sged", "std",
"sstd"), we decieded to use only numerical approximations.

regards,
Yohan