Minimum message length moving average time series data mining

This paper considers a criterion for selection of moving average (MA) time series models based upon the information-theoretic principle of minimum message length (MML). We derive an MML model selection criterion for invertible MA time series models using the Wallace and Freeman (1987) MML approximation, MML87. The MML model order selection performance is compared with other well-known model selection criteria such as Akaike's information criterion (AIC), corrected AIC (AICc), Bayesian information criterion (BIC), minimum description length (MDL, 1978), and the Hannan-Quinn (HQ) criterion. Our experiments show that the MML-based criterion achieves the lowest average mean squared prediction error and the best average log likelihood, and has the best ability to choose the true MA model order for smaller sample sizes.