Bayesian Analysis of Bivariate Mixture Transition Distribution Models

• Activity Number: 621
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Huiming Song*+ and Keh-shin Lii
• Companies: University of California at Riverside and University of California at Riverside
• Keywords: Bayesian Analysis ; BMTD models ; MCMC ; Dirichlet Process ; EM algorithm

Abstract

Bivariate Mixture Transition Distribution (BMTD) models are widely used in economics and business area, such as stock transaction prices and the transaction interarrival times. Usually the prices and times are studied seperately. However, as Engle (2000) shows, these two data are usually strongly associated. BMTD model is used to study them simultaneously. Previously, BMTD models are studied by EM algorithm. As knows, EM algorithm for mixture model has the problem of singularities, that is, the likelihood will goes to infinity as the denominator goes to zero. In my research, Bayesian analysisi of EM algorithm method is used to get consistent estimation. In the simulation, it's shown bayesian method can get better than non-bayesian methods. Also, MCMC can be used to estimate parameters since in this way, we needn't to prerestrict the number of mixture components as EM algorithm.