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

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.