Minimum Message Length Inference and Parameter Estimation of Auto regressive and Moving Average Models

This technical report presents a formulation of the parameter estimation and model selection problem for Autoregressive (AR) and Moving Average (MA) models in the Minimum Message Length (MML) framework. In particular, it examines suitable priors for both classes of models, and subsequently derives message length expressions based on the MML87 approximation. Empirical results demonstrate the new MML estimators outperform several benchmark parameter estimation and model selection criteria on various prediction metrics.