Order estimation for autoregressive models using criteria based on stochastic complexity

In this paper, we are interested in the order estimation of an autoregressive model using the information criterion developed by El Matouat and Hallin (1996), which is based on stochastic complexity. This criterion is a generalization of the Hannan and Quinn criterion and provides a convergence of the model order estimator, but it depends on a parameter that is sensitive to the sample size. In order to select the exact order of the candidate model, we propose a method for identifying the values of this parameter from the sample using the information contained in sub-samples of increasing size. To study the performance of the proposed method in comparison with the usual criteria, we simulated samples from autoregressive models on which we applied our procedure. Simulation results support the relevance of our procedure when compared to the Akaike criterion, the Hannan and Quinn criterion, and the Schwarz criterion.