Parametric model order estimation: a brief review

An important topic in parametric modelling is the question of the `correct´ model order. The correct order is not the true order, since the Wold Decomposition Theorem states that any finite moving average process can also be represented by an AR(∞) process. Nor is the correct order the one with minimum residual error as it is a monotonic decreasing function of the model order. The optimal order is the one which decreases the prediction error on a unobserved data set. FPE, AIC, and MDL are only three of many possible model order selection criteria. Many other methods have been proposed, however all are evaluated against these most popular estimators. It is important furthermore, when using any MO-estimator, to also consider the method used to estimate the model parameters. Methods, such as the Yule-Walker approach, require larger sample sizes and generally give worse residual estimates than the Burg method. This intrinsically results in higher model order estimates for the former. On the other hand, if some sensitivity is required, for instance in EEG applications, the Yule-Walker approach in conjunction with AJC, say, may give clearer results