Re: [Gretl-users] Help with GIG package

On Mon, 11 Jul 2011, Davor Horvatic wrote: Aaaaahhhh, nice, nice question. In short: no, there isn't. Longer answer: in the fuzzy and comfortable world of GARCH(1,1), the requirements alpha > 0 beta >= 0 (alpha + beta) < 1 are natural, because you want your conditional variances to be positive and finite for all t. Note that each of those requirements has a slight different reason: for example, alpha = 0 would make the model underidentified, so it's an absolute must. OTOH, the requirement (alpha + beta) < 1 applies to the TRUE parameters, whereas their ESTIMATES may happily violate that requirement in a finite sample: the point in the parameter space which maximises the likelihood may well be outside the admissible range just because your dataset ends with a massive volatility burst. Besides, you should also handle the case, which is frequent in practice, of parameters which go outside the admissible region during maximisation and eventually go back into it because the maximum is inside that region after all. In such a situation, what would you consider the "best" policy? Surely, you wouldn't want to hide the problem from the user, so just printing out something like "I'm sorry, your estimates are outside the admissible region" would be a pathetically patronizing decision from the software. In my opinion, you want to treat these results for what they are: a finite-sample oddity if your model is right or (more likely) an indication that perhaps your model wasn't the best choice after all. So I thought: ok, let's put no constraints on the parameters and just issue a warning if the algorithm stops at some unorthodox point. This is easy for a GARCH(1,1) model: for GARCH(p,q) models, this is more complex, but still possible (see Nelson and Cao (1992), JBES). But then, what do you do when you have models with exogenous variables in the volatility equation? Or non-GARCH models? I am not aware of a generalisation of the Nelson-Cao conditions for the APARCH model (pointers appreciated, if any of you know of any). Maybe we could treat the GARCH case specially and write a function for checking the Nelson-Cao conditions? That should be quite easy to do. Any volunteers? Riccardo (Jack) Lucchetti Dipartimento di Economia Università Politecnica delle Marche r.lucchetti(a)univpm.it http://www.econ.univpm.it/lucchetti