[Gretl-users] maximum like. conditions

Riccardo (Jack) Lucchetti r.lucchetti at univpm.it
Mon Nov 30 02:58:47 EST 2009

On Sun, 29 Nov 2009, Allin Cottrell wrote:

> ;-) This is a subtle bug (if it's a bug; I'm not sure) with an
> easy workaround.  With the initialization
> scalar alpha = 0.4
> scalar beta = 0
> The "check" condition -- alpha>0 && beta>0 -- is violated on the
> first iteration.  Therefore the formula for "ll" comes down to
> ll = NA
> This generates a scalar value, which is not allowed in the mle
> context.  The fix is to initialize such that the check is
> satisfied on the first round, e.g.
> scalar beta = 0.001

Not really relevant here, but the constraints on alpha and beta in a 
garch(1,1) model are not exactly the same. Alpha needs to be strictly 
positive (otherwise the model is unidentified), but beta can be 0, so 
initialising it at 0 is perfectly legitimate. The check should be written 
as (alpha>0) && (beta>=0). Sorry for being pedantic.

Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche

r.lucchetti at univpm.it

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