Moddemeijer: an Efficient Algorithm for Selecting Optimal Configurations of Ar-coefficients

There exists an essential difference between the correct Auto Regressive (AR) model and the optimal ARmodel. 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 ARparameter 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 Gauß-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. Keywords—AIC, Akaike criterion, AR, autoregressive processes, composite hypothesis, maximum likelihood, model order, system identification, time series analysis.