Re: [Gretl-devel] Problem with Ljung-Box Q pvalues
On Tue, 3 Mar 2015, Sven Schreiber wrote:
Am 03.03.2015 um 16:05 schrieb Allin Cottrell:
>
> I was thinking along the same lines as in your patch for library.c in
> the GUI, but it's not that simple. Two things have to be answered.
>
> 1) What's the appropriate generalization of "m-p-q" for cases such as
> "gappy" arma and seasonal arma? Is it just the total number of AR and MA
> coefficients estimated?
Yes, AFAICS that's the idea. I'm saying "AFAICS" because given the
lagged
endogenous terms in an ARMA model I have never really understood why this Q
test should be used rather than an LM-type test. But that's a different
discussion I guess.
Well, the vague idea is that, although exact ML estimates don't satisfy
this exactly, the first-order conditions for ML force a few
autocorrelations to be 0 by construction: for example, think of a MA(1)
model: the FOC is simply \sum u_t u_{t-1} = 0 (well, not exactly, but you
get the idea). So, in terms of "moment conditions", this is not a valid
one you can use when you contruct a test statistic and therefore you
should drop it.
The problem is that this reasoning becomes messy when you have mixed AR/MA
models, especially with gaps in the lag structure.
(BTW I'm not sure what you mean by seasonal ARMA or how it
differs from a
standard ARMA.)
A seasonal ARMA is "gappy" by construction.
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Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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