On Wed, 20 Jul 2011, Davor Horvatic wrote:
Dear Jack,
I want first to thank you for detailed answer on the restriction of the GARCH parameters. I will look to dig some more details out if I can.
I put some of that into the gig pdf doc; when CVS comes back up and you can download it, your comments are welcome.
In this post I'll be as detailed as I can be. In attachment you will find
time series used to reproduce numbers mentioned below. I'm wondering
why is there discrepancy in std errors between GIG on one side and Eviews
on the other. I.e. to be precise difference between Sandwich (default) and OPG or
Hessian as VCV method. As you will see I get similar results for Eviews and GIG
for all cases except for default Sandwich estimator.
[...]
Allin's script shows very clearly how things are done in gig. If you ask me if I believe that's correct, my answer is yes. If you ask me if everything else is wrong, my answer is no. As Allin said, there is a number of asymptotically equivalent ways to obtain robust vcv matrices; the trouble is, they may be very different from one another in finite samples (and yes, 2746 observations may well be "not enough").
One possible difference is, as Allin said, the type of bread you use in the sandwich: Hessian or information matrix? Another difference may come from the fact that I used the delta method to compute the vcv for the alternate parametrisation. Again, this is a quadratic form with the Jacobian acting as the "bread" and the vcv for the original parametrisation as the "ham". The choice of the type of ham should make no difference asymptotically, but in finite samples it does.
Moreover, your model seems to be misspecified in at least one respect: if you run the following script fragment
<hansl>
foo = gig_setup(ld_WIG, 3)
gig_estimate(&foo, 0)
series u = foo["stduhat"]
summary u
normtest u --all
gig_set_dist(&foo, 1)
gig_estimate(&foo)
</hansl>
you will see that assuming conditional normality is likely to be a very bad idea; actually, if the "true" distribution is t with 5.9 degrees of freedom I'm not even sure that the conditions for asymptotic normality are satisfied (I'd need to check). In a setting such as this, I'm not at all surprised that alternative choices for robust inference may yield largely different results.
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti@univpm.it
http://www.econ.univpm.it/lucchetti
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