Order selection for AR models by predictive least squares

A criterion is presented for selecting the order of autoregressive models that, unlike the existing criteria, is amenable to online or adaptive operation. It is based on the predictive least squares (PLS) principle and is implemented in a computationally efficient way by predictive lattice filters. The consistency of the criterion is proved, and its performance is demonstrated by computer simulations. Assuming the data to be generated by an AR model of order p, the order selection criterion should select the correct order p with probability that converges to 1 as the sample size grows to infinity. It is proved that the PLS criterion is indeed consistent, thereby giving a solid justification for the criterion. Simulation results that demonstrate the performance of the PLS criterion in comparison to H. Akaike´s AIC (1973) and the MDL criteria of J. Rissanen (1978) and G. Schwarz (1978) are given