Variance Estimates and Model Selection

Published in: International Econometric Review Vol 2, issue 2. [link to journal]

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co=authored by Siddika Basci and Arzdar Kiraci.

The large majority of the criteria for model selection are functions of the usual

variance estimate for a regression model. The validity of the usual variance

estimate depends on some assumptions, most critically the validity of the model

being estimated. This is often violated in model selection contexts, where model

search takes place over invalid models. A cross validated variance estimate is

more robust to specification errors (see, for example, Efron, 1983). We consider

the effects of replacing the usual variance estimate by a cross validated variance

estimate, namely, the Prediction Sum of Squares (PRESS) in the functions of

several model selection criteria. Such replacements improve the probability of

finding the true model, at least in large samples.

Key words: Autoregressive process, Lag order determination, Model selection

criteria, Cross validation

JEL Classifications: C13, C15, C22, C52