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AR-order estimation by testing sets using the Modified Information Criter
ion

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

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Abstract

The Modified Information Criterion (MIC) is an Akaike-like criterion which
allows performance control by means of a simple a priori defined parameter,
the upper-bound on the error of the first kind (false alarm probability).
The criterion MIC is for example used to estimate the order of
Auto-Regressive (AR) processes. The criterion can only be used to test
pairs of composite hypotheses; in an AR-order estimation this leads to
sequential testing. Usually the Akaike criterion is used to test sets of
composite hypotheses. The difference between sequential and set testing
corresponds with the difference between searching the first local and the
global minimum of the Akaike criterion. We extend the criterion MIC to
testing a composite null-hypothesis versus a set of composite alternative
hypotheses; these alternative hypotheses form a sequence where every element
introduces one additional parameter. The theory is verified by simulations
and is compared with the Akaike criterion used in sequential and set
testing. Due to the excellent correspondence between the theory and the
experimental results we consider the AR-model order estimation problem
for low order AR-processes with Gaussian white noise as solved.

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Keywords

AIC, Akaike criterion, AR, autoregressive processes, composite
hypothesis, maximum likelihood, model order, system
identification, time series analysis.

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Published

*AR order estimation by testing sets using the Modified Information Criterion,
*,
BibTeX

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