A note on the order selection of mixture periodic autoregressive models

In this note, we consider the problem of order selection of Mixture Periodic Autoregressive (MPAR) models. These models are among the most powerful tools for modeling some stylized features exhibited by many time series such as multimodality, tail heaviness, change in regime, asymmetry and periodicity in the conditional mean. We propose to use a variant of the Akaike information criterion (AIC), for MPAR model selection, based on complete-data rather than incomplete-data and which different from the standard criteria. This variant has been proposed by Cavanaugh and Shumway (1998) for model selection in the presence of incomplete data. We compare the performance of the proposed criterion to that of the traditional AIC criterion and certain other competitors in a simulation study.