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.
Keywords: Autoregressive process, Lag order determination, Model selection criteria, Cross validation.
JEL Classifications: C13, C15, C22, C52.
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1Sidika Basci, Statistical, Economic and Social Research and Training Center for Islamic Countries
(SESRTCIC), Department of Statistics, Attar Sokak, No:4, 06700, Gaziosmanpasa, Ankara, Turkey, (email:sbasci@sesrtcic.org), Tel. + 90312 4686172/308, Fax: + 90312 4673458.
2Asad Zaman, International Institute of Islamic Economic, International Islamic University of Islamabad, Pakistan.
3Arzdar Kiraci, Baskent University, Department of Economics, 06533 Baglica, Ankara, Turkey.