An efficient algorithm for selecting optimal configurations of AR-coefficients

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:


There exists an essential difference between the correct Auto Regressive (AR) model and the optimal AR-model. We try to find an optimal model balancing between flexibility, using many AR-parameters, and low variance, using only a few AR-parameters. We select an optimal AR-parameter configuration consisting of zero and non-zero parameters given a maximum AR-order. This optimal configuration will be selected using a Modified Information Criterion (MIC) which is closely related to Akaike's criterion (AIC). This MIC allows an a priori selection of the probability of estimating too many parameters.

We present the theoretical foundation of the method and verify this method by simulations. The method is based on pivoting the Hessian matrix by Gau\ss-Jordan pivots. As a result we can now select an optimal parameter configuration with an a priori probability of selecting a configuration with a too large number of parameters given an a priori selected maximum AR-order.


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


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