# st: RE: Re: adjusted r square

 From "Nick Cox" To Subject st: RE: Re: adjusted r square Date Wed, 21 Feb 2007 12:12:47 -0000

No dispute from me, and this is interesting!

But what is here is par for the course: a mix of
asymptotic arguments and an appeal to simulations
for a special case that need not be my model.

Nick
n.j.cox@durham.ac.uk

Kit Baum

> This is not merely conjecture. Greene (Econometric Analysis,
> 5th ed.)
> p.565 "The Akaike information criterion retains a positive
> probability of leading to overfitting even as T -> \infty. In
> contrast, SC(p) [Schwarz or Bayes IC] has been seen to lead to
> underfitting in some finite sample cases."
>
> If you do a Monte Carlo simulation in which the true DGP is an AR(p)
> model, and apply the AIC (pretending that you do not know the
> appropriate value of p) to determine the lag order, there is a
> positive probability that AIC will signal a lag length > p. That is
> what is 'widely agreed' because of that positive bias. Of
> course, the
> theory of specification error suggests that you would be better off
> estimating an overparameterized model than an
> underparameterized model.

On Feb 21, 2007, at 2:33 AM, Nick wrote:
>
> >  I regularly read advice such as that AIC is widely agreed
> > to give the wrong answer, to which the reaction has to be,
> How do they
> > know?

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