Bayesian Time Series Analysis of Structural Changes in Level and Trend

Abstract

In this article we consider the problem of detecting changes in level and trend in time series model in which the number of change-points is unknown. The approach of Bayesian stochastic search model selection is introduced to detect the configuration of changes in a time series. The number and positions of change-points are determined by a sequence of change-dependent parameters. The sequence is estimated by its posterior distribution via the maximum a posteriori (MAP) estimation. Markov chain Monte Carlo (MCMC) method is used to estimate posterior distributions of parameters. Some actual data examples including a time series of traffic accidents and two hydrological time series are analyzed.

Keywords:

• Bayesian stochastic search selection
• Bayesian time series analysis
• MCMC
• M-H algorithm
• Structural changes

Mathematics Subject Classification:

• 62E15
• 62H99

Acknowledgment

This research was supported by a research grant from The Hong Kong Polytechnic University Research Committee. The third author's research was also supported by the National Natural Science Foundation of China (No. 11171117) and the Natural Science Foundation of Guangdong Province of China (No. S2011010002371).