I have just noticed that Chapter 25 of the user's guide contains a very good discussion of the transformations of the AIC.

---------- Forwarded message ----------
From: John C Frain <frainj@gmail.com>
Date: 2 March 2018 at 12:56
Subject: Re: [Gretl-users] Function of the AIC in VAR lag selection (Marvin Berndt) (Marvin Berndt)
To: Gretl list <gretl-users@lists.wfu.edu>


Chapter 25 (Model Selection Criteria) in the Gretl user's guide defines the AIC as 

AIC = -2‘(θ ˆ) + 2k - (Pasted formula not quite correct - see Guide ) 

 The formulas that you quote are both monotonic transformations of this formula.  That is the order of the models is not changed under these transformations.  All formulas lead to the same conclusion.  I would presume that some formulas are easier to calculate for certain types of models. 

I would also comment that estimating 10 coefficients and  co-variances  with 10  observations (and 2 obs to initialize) will not lead to reliable results.


John C Frain
3 Aranleigh Park

On 2 March 2018 at 12:21, Sven Schreiber <svetosch@gmx.net> wrote:
Am 02.03.2018 um 12:36 schrieb Marvin Berndt:
Dear Ioannis,
the residual in the Excel-sheets are those from the VAR regresison. I extracted them from the VAR regression Output via '/Save --> Residuals from equation 1/2/'. I used those residuals in order to try to recreate the AIC in gretl.

With such a short sample I suspect it makes a big difference whether 1/T or 1/(T-K) is used for the (co)variance calculation. Both variants are "correct" in that the method is for large samples anyway.

There was a discussion on this (ore the devel) mailing list about whether to apply a d.o.f.-correction for VARs but I cannot find it. I agree it could be documented better, the VAR chapter in the guide is --alas-- still not finished.
I _believe_, however, that gretl for VARs does it without this small-sample correction (this would also apply to the $sigma accessor, to those who know what that is).

In principle we could all look it up in the source, right? Hehe. (Apart from the fact that currently sourceforge is not accessible.)

cheers,
sven

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