Page 1 of 1
ARMA and degrees of freedom
Posted: Thu Feb 18, 2010 6:06 am
by Swansea
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?
Re: ARMA and degrees of freedom
Posted: Tue Feb 23, 2010 3:40 pm
by Swansea
Does anyone have any views on this?
Re: ARMA and degrees of freedom
Posted: Tue Mar 16, 2010 12:33 pm
by Swansea
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.
Re: ARMA and degrees of freedom
Posted: Wed Mar 17, 2010 9:29 am
by EViews Gareth
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).
Re: ARMA and degrees of freedom
Posted: Thu Mar 18, 2010 12:21 pm
by Swansea
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. :?