ARMA and degrees of freedom

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Swansea
Posts: 9
Joined: Wed Feb 17, 2010 4:51 pm

ARMA and degrees of freedom

Postby Swansea » Thu Feb 18, 2010 6:06 am

Just a quick question. When estimating an ARMA model with an intercept, the AIC uses the intercept in its calculation but the Q-stats do not.
For example, an ARMA(1,1) with intercept uses k=3 in the calculation of the penalty attached to the log-likelihood, but the Q-stats use k=2 in the calculation of their degrees of freedom. Should the df be adjusted?

Swansea
Posts: 9
Joined: Wed Feb 17, 2010 4:51 pm

Re: ARMA and degrees of freedom

Postby Swansea » Tue Feb 23, 2010 3:40 pm

Does anyone have any views on this?

Swansea
Posts: 9
Joined: Wed Feb 17, 2010 4:51 pm

Re: ARMA and degrees of freedom

Postby Swansea » Tue Mar 16, 2010 12:33 pm

Given the absence of a reply to my message, I wondered whether it simply reflects a misunderstanding on my part- and hence does not need an answer!
Any comments would be much appreciated.
Thank you.

EViews Gareth
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Joined: Tue Sep 16, 2008 5:38 pm

Re: ARMA and degrees of freedom

Postby EViews Gareth » Wed Mar 17, 2010 9:29 am

Hi.

Sorry for the long quiet period on this.

That particular Q-stats correction has been in EViews for 20 years, so it took a while to discover why it was done. Unfortunately I haven't had a huge amount of luck in finding the reason, other than "the original Box-Jenkins theories stated that Q-stats should be adjusted for ARMA terms". I can't really say whether there should also be adjustments made for the constant (although it does seem to be a reasonable statement).

Swansea
Posts: 9
Joined: Wed Feb 17, 2010 4:51 pm

Re: ARMA and degrees of freedom

Postby Swansea » Thu Mar 18, 2010 12:21 pm

Dear Gareth

Many thanks for the post.

It is a bit of an uncertain issue, at least as far as I am concerned.
I was reading a text the other day which explicitly referred to including the constant when considering Box-Pierce Q-stats, but was then, at least in my reading of it, mixed on its inclusion of the constant in its application of the Ljung-Box statistic. :?


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