Re: [Rd] The constant part of the log-likelihood in StructTS

From: Ravi Varadhan <>
Date: Fri, 04 May 2012 01:50:46 +0000

Thanks, Tom, for the reply as well as to the reference to Claeskens & Hjort.


From: Thomas Lumley []
Sent: Thursday, May 03, 2012 4:41 PM
To: Mark Leeds
Cc: Ravi Varadhan; Subject: Re: [Rd] The constant part of the log-likelihood in StructTS

On Thu, May 3, 2012 at 3:36 AM, Mark Leeds <> wrote:
> Hi Ravi: As far as I know ( well , really read ) and Bert et al can say
> more , the AIC is not dependent on the models being nested as long as the
> sample sizes used are the same when comparing. In some cases, say comparing
> MA(2), AR(1), you have to be careful with sample size usage but there is no
> nesting requirement for AIC atleast, I'm pretty sure.

This is only partly true. The expected value of the AIC will behave correctly even if models are non-nested, but there is no general guarantee that the standard deviation is small, so AIC need not even asymptotically lead to optimal model choice for prediction in arbitrary non-nested models.

Having said that, 'nearly' nested models like these are probably ok. I believe it's sufficient that all your models are nested in a common model, with a bound on the degree of freedom difference, but my copy of Claeskens & Hjort's book on model selection and model averaging is currently with a student so I can't be definitive.


Thomas Lumley
Professor of Biostatistics
University of Auckland
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