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The Least-Squares-Forward-Backward (LSFB) method for estimating the parameters of the autoregressive (AR) model is considered and new theoretical approximations for expectations of the prediction error and the residual variance are derived. These results are used for modifying the AR order selection criteria FPE and AIC. The performance of these modified criteria is compared with other AR order selection criteria using simulated data. The results of these performance comparisons show that the new criteria have better performance in the finite sample case.