New autoregressive (AR) order selection criteria based on the prediction error estimation

The most important problem in data modeling using the AR model is the order selection. Some AR order selection criteria estimate the prediction error and choose the order that minimizes this estimated prediction error. All of these criteria use the same formula for estimating the prediction error from the residual variance for all AR models. However, experimental results show that the relationship between the prediction error and the residual variance depends on the AR model. In this paper, we introduce new formulas for estimating the prediction error using the residual variance. These formulas depend on the AR model, and are obtained through assuming a white Gaussian noise as the input noise to the AR model and assuming that the least-squares-forward (LSF) method is used for estimating the AR coefficients. The performance of the new order selection criteria introduced in this paper is compared with other AR order selection criteria using simulated data. Results show that the new criteria have good performance in estimating the prediction error and in selecting an appropriate order for the AR model.

► New formulas for estimating the prediction error are introduced for autoregressive processes.
► The proposed formulas depend on the autoregressive process under consideration.
► New autoregressive order selection criteria are proposed.