Bayesian Model Order Selection of Vector Moving Average Processes

Abstract

The authors propose an approximate convenient Bayesian technique to identify the order of vector time series generated by moving average processes. The foundation of the proposed technique is to approximate the likelihood function by a matrix normal-Wishart distribution on the parameter space. Based on the approximated likelihood function, the marginal posterior probability mass function of the model order is developed in an analytic convenient form. Then it is possible to easily evaluate the posterior probabilities of the model order and choose the order at which the posterior mass function attains its maximum to be the identified order. A simulation study, with 3 different priors, was conducted to demonstrate the idea of using the proposed Bayesian technique and check its adequacy in handling the identification problem. The numerical efficiency of the proposed technique is also compared to the AIC technique. In addition, the proposed Bayesian technique was used to identify the well known bivariate data generated by Tiao et al. (1979). The inspection of the numerical results supports the adequacy of using the proposed Bayesian technique to identify the order of vector moving average processes.

Keywords:

• AIC technique
• Identification
• Likelihood function
• Matrix normal-Wishart distribution
• Probability mass function
• Vector moving average processes

Mathematics Subject Classification:

• Primary 37M10
• Secondary 62F15