AR order selection in the case when the model parameters are estimated by forgetting factor least-squares algorithms

During the last decades, the use of information theoretic criteria (ITC) for selecting the order of autoregressive (AR) models has increased constantly. Because the ITC are derived under the strong assumption that the measured signals are stationary, it is not straightforward to employ them in combination with the forgetting factor least-squares algorithms. In the previous literature, the attempts for solving the problem were focused on the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the predictive least squares (PLS). In connection with PLS, an ad hoc criterion called SRM was also introduced. In this paper, we modify the predictive densities criterion (PDC) and the sequentially normalized maximum likelihood (SNML) criterion such that to be compatible with the forgetting factor least-squares algorithms. Additionally, we provide rigorous proofs concerning the asymptotic approximations of four modified ITC, namely PLS, SRM, PDC and SNML. Then, the four criteria are compared by simulations with the modified variants of BIC and AIC.