Minimum Message Length Autoregressive Moving Average Model Order Selection

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.

[1]  G. Box,et al.  The likelihood function of stationary autoregressive-moving average models , 1979 .

[2]  Leigh J. Fitzgibbon,et al.  Minimum message length autoregressive model order selection , 2004, International Conference on Intelligent Sensing and Information Processing, 2004. Proceedings of.

[3]  Farshid Vahid.  Partial pooling: A possible answer to "To pool or not to pool" , 1999 .

[4]  D. Dowe,et al.  Minimum message length moving average time series data mining , 2005, 2005 ICSC Congress on Computational Intelligence Methods and Applications.

[5]  O. Barndorff-Nielsen,et al.  On the parametrization of autoregressive models by partial autocorrelations , 1973 .

[6]  D. Rosadi,et al.  Minimum Message Length in Hybrid ARMA and LSTM Model Forecasting , 2021, Entropy.

[7]  Peter J. Brockwell,et al.  Gaussian Maximum Likelihood Estimation for Arma Models I: Time Series , 2006 .

[8]  The relationship between the conditional sum of squares and the exact likelihood for autoregressive moving average models , 1997 .

[9]  J. W. Miller.  EXACT MAXIMUM LIKELIHOOD ESTIMATION IN AUTOREGRESSIVE PROCESSES , 1995 .

[10]  Gregory C. Reinsel,et al.  An Exact Maximum Likelihood Estimation Procedure for Regression- ARMA Time Series Models with Possibly Nonconsecutive Data , 1986 .

[11]  E. Ward.  A review and comparison of four commonly used Bayesian and maximum likelihood model selection tools , 2008 .

[12]  O. D. Anderson,et al.  On the inverse of the autocovariance matrix for a general moving average process , 1976 .

[13]  David L. Dowe,et al.  Minimum Message Length and Kolmogorov Complexity , 1999, Comput. J..

[14]  Chi Kuen Wong.  Minimum message length inference with application to genome-wide association studies data , 2019 .

[15]  D. Piccolo.  THE SIZE OF THE STATIONARITY AND INVERTIBILITY REGION OF AN AUTOREGRESSIVE‐MOVING AVERAGE PROCESS , 1982 .

[16]  C. S. Wallace,et al.  An Information Measure for Classification , 1968, Comput. J..

[17]  Guy Mélard,et al.  Computation of the Fisher information matrix for time series models , 1995 .

[18]  Peter J. Brockwell,et al.  Gaussian maximum likelihood estimation for ARMA models II: Spatial processes , 2006 .

[19]  C. S. Wallace,et al.  Estimation and Inference by Compact Coding , 1987 .