Optimal autoregressive (AR) model order selection in the sense of predictive error

There are many model order selection criteria that have been applied to the AR order selection problem. Some of these criteria such as FPE, FSC, MFSC, and FPEF are based on minimizing the prediction error, but we are not able to claim that these criteria are optimal in the sense of prediction error. Here, an optimal predictive order selection criterion for AR model will be obtained when input noise of model is white Gaussian noise. Then, we will apply this criterion to simulated data and compare its performance with that of other AR order selection criteria. Simulation results show that the new criterion has lower prediction error than the other AR order selection criteria.