Bayes Estimation Of Change Point Problems In The Ar (1) And Arch (1) Model

This paper discusses Bayesian method in AR(1) change-point models and ARCH(l) change-point models. The first chapter is the introduction of the background of change-point problem in time series analysis.In chapter 2,we get a closed form for all the parameters in Bayesian method of AR(1) by using the properties of t-distribution and IG-distribution. We provide a numerical simulation to prove our method and compare it with MLE method. And we apply the method to the series of daily columns of Shanghai Securities Composite Index. We find the change point of this series successfully.In chapter 3, we discuss change-point problem in ARCH(1) models. We get the Maximum Likelihood Estimation and Bayesian Estimation for ARCH(1) model. In the study of Bayesian Estimation, it's difficult to get closed form for parameters, so we choose Gibbs Sampling. For full condition distribution of all parameters are log-concave, we use Adaptive Rejection Sam-pling(ARS) to get posterior distributions of the parameters. We also provide a numerical simulation to prove our method and apply our method to the series of daily columns of Shanghai Securities Share A Index.