A Bayesian structural-change analysis via the stochastic approximation Monte Carlo and Gibbs sampler

Abstract

In this article, we propose a Bayesian approach to estimate the multiple structural change-points in a level and the trend when the number of change-points is unknown. Our formulation of the structural-change model involves a binary discrete variable that indicates the structural change. The determination of the number and the form of structural changes are considered as a model selection issue in Bayesian structural-change analysis. We apply an advanced Monte Carlo algorithm, the stochastic approximation Monte Carlo (SAMC) algorithm, to this structural-change model selection issue. SAMC effectively functions for the complex structural-change model estimation, since it prevents entrapment in local posterior mode. The estimation of the model parameters in each regime is made using the Gibbs sampler after each change-point is detected. The performance of our proposed method has been investigated on simulated and real data sets, a long time series of US real gross domestic product, US uses of force between 1870 and 1994 and 1-year time series of temperature in Seoul, South Korea.