On Wed, 4 Mar 2015, Sven Schreiber wrote:
>> So the whole business becomes even murkier when m is so small
that
>> m-p-q becomes negative. Also using dof=m instead of m-p-q is not wrong
>> asymptotically I believe, it's all "just" about small-sample
>> corrections (which can be very important of course though).
> If your T is very very large you may calculate the Q stat for a very
> large m, and then given p and q not very large, a chi-square(m) and
> chi-square (m-p-q) may be similar. But usually we don't have so large T
> and we are interested in relatively low values of m. From m>p+q we have
> enough dof and the Q stat for a residuals series may have sense, and
> the asymptotic distribution is chi-square (m-p-q) different from the
> chi-square(m).
I'm tempted to dive into the details, but not now; let me just say that this
whole discussion has not weakened my skepticism about using the Q-type tests
for residuals (as opposed to raw original series).
At the risk of being boring, let me say: I believe the only solid way to
analyse the issue is to view the Q statistic as a conditional moment test.
I'd love to go into greater detail, but I have to run to class (to
paraphrase Pierre de fermat).
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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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