Minimum Message Length Autoregressive Moving Average Model Order Selection

TL;DR

This paper introduces a Minimum Message Length (MML) criterion for selecting ARMA model orders, demonstrating its superior performance over traditional criteria like AIC, BIC, and HQ in predicting time series data.

Contribution

The paper develops and evaluates an MML-based criterion specifically for ARMA model order selection, showing improved accuracy over existing methods.

Findings

MML87 outperforms AIC, BIC, and HQ in model selection.

Models selected by MML87 have lower prediction errors.

MML87 achieves lower mean squared errors across various sample sizes.

Abstract

This paper derives a Minimum Message Length (MML) criterion for the model selection of the Autoregressive Moving Average (ARMA) time series model. The MML87 performances on the ARMA model compared with other well known model selection criteria, Akaike 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.