Testing composite hypotheses applied to AR-model order estimation; the Akaike-criterion revised

R. Moddemeijer

University of Groningen, Department of Computing Science,
P.O. Box 800, NL-9700 AV Groningen, The Netherlands,
phone: +31.50.363 3940 - fax: +31.50.363 38005 - e-mail: rudy@cs.rug.nl

Abstract

Akaike's criterion is often used to test composite hypotheses; for example to determine the order of a priori unknown Auto-Regressive and/or Moving Average models. Objections are formulated against Akaike's criterion and some modifications are proposed. The application of the theory leads to a general technique for AR-model order estimation based on testing pairs of composite hypotheses. This technique allows performance control by means of a simple parameter, the upper-bound on the error of the first kind (false alarm probability).

The presented simulations and the theoretical elaboration improve the understanding of the problems and limitations of techniques based on the Akaike criterion. Due to the excellent correspondence between the theory and the experimental results we consider the in AR-model order estimation problem for low order AR-processes with Gaussian white noise as solved.

Keywords

AIC, Akaike criterion, AR, ARMA, autoregressive processes, composite hypothesis, entropy, maximum likelihood, model order, Neyman-Pearson, system identification, time series analysis.

Published

Testing composite hypotheses applied to AR order estimation; the Akaike-criterion revised, BibTeX

Related work

Conference presentation: Testing composite hypotheses applied to AR order estimation; the Akaike-criterion revised
Conference presentation: Testing composite hypotheses applied to AR order estimation; the Akaike-criterion revised
Earlier work: Testing composite hypotheses
Earlier work: From maximum likelyhood to an entropy estimate
Earlier work: Testing composite hypotheses; the Akaike-criterion revised
Later work: AR order estimation by testing sets using the Modified Information Criterion
Later work: An efficient algorithm for selecting optimal configurations of AR-coefficients
Later work: Application of information criteria to AR order estimation

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