New autoregressive model order selection criterion using same-realization predictions

The final prediction error (FPE) criterion is an asymptotic estimate of the prediction error that is used for autoregressive (AR) model order selection. In this paper, we derive a new theoretical estimate of the prediction error for the same-realization predictions. This estimate is derived for the case that the Least-Squares-Forward (LSF) method (the covariance method) is used as the AR parameter estimation method. This result is used for obtaining a new version of the AR order selection criterion FPE in the finite sample case. The performance of this criterion is compared with that of the conventional FPE criterion using simulated data. The results of this comparison show that the performance of the proposed criterion is better than FPE.