From r.lucchetti@univpm.it Thu May 27 13:14:22 2010
From: Riccardo (Jack) Lucchetti <r.lucchetti@univpm.it>
To: gretl-devel@gretlml.univpm.it
Subject: Re: [Gretl-devel] BIC in ols
Date: Thu, 27 May 2010 19:14:20 +0200
Message-ID: <alpine.DEB.2.00.1005271857460.32038@ec-4.econ.univpm.it>
In-Reply-To: 1274977327.2116.15.camel@U001082
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On Thu, 27 May 2010, Ignacio Diaz-Emparanza wrote:

> I am a little confused about the behaviour of AIC, HQC and BIC in
> the standard ols command. I estimated some AR(p) models with different p
> values with the 'ols' and the 'var' commands. The last with only one
> variable which I know it is not designed for, but ... it works.
>
> I see that the BIC obtained through both commands:
>
> 1- are not the same. I suspect may be some different scale factor in the
> formulas but this should not be a problem.

Well spotted: in fact, when we compute the information criteria for VARs, 
we use as the sample size the total data span (T), whereas for OLS we use 
the number of datapoints actually used (T-number of lags). To see what 
I'm talking about, try this little modification of your script:

<script>
#AR(p) selection
function void ARF(series y, scalar maxorder)
     matrix C=zeros(maxorder,3)
     loop i=1..maxorder
         var i y --quiet
         genr C[i,1]=i
         genr C[i,2] = $bic
         list xlist = lags(i,y)
         ols y 0 xlist --quiet
         genr C[i,3]= $bic / $T
     end loop
C
end function

open data9-3.gdt
Y=diff(reskwh)
Y=sdiff(Y)
ARF(Y, 30)
</script>

> 2- leads to different specification, and yes, this is a problem. In 
> concrete, the BIC in ols would suggest the maximum number of lags, and 
> this does not seem to be correct if one have a look at the correlograms.

I agree it is a problem, but only to an extent: information criteria are 
likelihood-based, and as such have asymptotic validity only. Allin thinks 
that this could be the outcome of the policy of "trying to agree as much as 
possible with other packages". If package A uses T and package B uses T-k, 
well... the issue "internal consistency vs agreement with others" has been 
debated to death and I really wouldn't know what to say.


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

r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti

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