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A derivation of the information criteria for selecting autoregressive models

Published online by Cambridge University Press:  01 July 2016

R. J. Bhansali
R. J. Bhansali*
Affiliation:
University of Liverpool
*
∗Postal address: Dept of Statistics and Computational Mathematics, University of Liverpool, Victoria Building, Brownlow Hill, P.O. Box 147, Liverpool L69 3BX, UK.
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Abstract

The Akaike information criterion, AIC, for autoregressive model selection is derived by adopting −2T times the expected predictive density of a future observation of an independent process as a loss function, where T is the length of the observed time series. The conditions under which AIC provides an asymptotically unbiased estimator of the corresponding risk function are derived. When the unbiasedness property fails, the use of AIC is justified heuristically. However, a method for estimating the risk function, which is applicable for all fitted orders, is given. A derivation of the generalized information criterion, AICα, is also given; the loss function used being obtained by a modification of the Kullback-Leibler information measure. Results paralleling those for AIC are also obtained for the AICα criterion.

Keywords

AICAICαAUTOREGRESSIVE PROCESSORDER DETERMINATIONKULLBACK–LEIBLER INFORMATION MEASURE
Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 2 , June 1986 , pp. 360 - 387
Copyright
Copyright © Applied Probability Trust 1986 

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