Minimum Message Length Autoregressive Moving Average Model Order Selection

Abstract

This paper derives a Minimum Message Length (MML) criterion for the model selection of the Autoregressive-Moving-Average (ARMA) time series model. The model selection criterion using Wallace and Freeman's (1987) MML approximation, which is an extended version of MML, called MML87. The MML87 performances on the ARMA model compared with other well-known model selection criteria, Akaike's Information Criterion (AIC), Corrected AIC (AICc), Bayesian Information Criterion (BIC), and Hannan-Quinn (HQ). The experimental results show that the MML87 is outperformed the other model selection criteria as it select most of the models with lower prediction errors and the models selected by MML87 to have a lower mean squared error in different in-sample and out-sample sizes.