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

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

other publications