Finite Sample FPE and AIC Criteria for Autoregressive Model Order Selection Using Same-Realization Predictions

A new theoretical approximation for expectation of the prediction error is derived using the same-realization predictions. This approximation is derived for the case that the Least-Squares-Forward (LSF) method (the covariance method) is used for estimating the parameters of the autoregressive (AR) model. This result is used for obtaining modified versions of the AR order selection criteria FPE and AIC in the finite sample case. The performance of these modified criteria is compared with other same-realization AR order selection criteria using simulated data. The results of this comparison show that the proposed criteria have better performance.