Ar order selection with Information Theoretic Criteria based on localized estimators

As the Information Theoretic Criteria (ITC) for AR order selection are derived under the strong hypothesis of stationarity of the measured signals, it is not straightforward to utilize them in conjunction 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). This study provides a variant of the Predictive Densities Criterion (PDC) that it is compatible with the forgetting factor least-squares algorithms. We also introduce a modified version of the very new Sequentially Normalized Maximum Likelihood (SNML) criterion. Additionally, we give rigorous proofs for results concerning PLS and SNML.