A corrected FPE criterion for autoregressive processes

One of the approaches that can be used in autoregressive (AR) model order selection is to choose the order that minimizes the prediction error. The final prediction error (FPE) criterion uses this approach in order selection. Unfortunately, this criterion has poor performance in the finite sample case. In this paper, new theoretical approximations are derived for the expectations of residual variance and prediction error of least-squares-forward (LSF) AR parameter estimation method. These approximations are specially useful in the finite sample case and are derived for AR processes with arbitrary statistical distributions. A corrected version of FPE is derived using these approximations. The performance of this corrected version in the finite sample case is evaluated and compared with FPE using simulations. Simulation results show that the performance of the proposed criterion is much better than FPE.