Finite Sample Criteria for Autoregressive Model Order Selection

The existing theoretically derived order selection criteria for autoregressive (AR) processes have poor performance in the finite sample case. In this paper, the least-squares-forward (LSF) is considered as the AR parameter estimation method, and new theoretical approximations are derived for the expectations of residual variance and prediction error. These approximations are especially useful in the finite sample case and are derived for AR processes with arbitrary statistical distributions. New order selection criteria for AR processes are derived using these approximations. In a simulation study, the performance of the proposed criteria relative to other criteria is examined in the finite sample case. Simulation results show that the performance of the proposed criteria is much better than the other theoretically derived criteria.