Multiple Change-point Detection For The Scale Parameter In Gamma Distribution Based On RJMCMC

The research of change point has obtained more and more attention in meteorology and finance fields.In this paper,we discuss the problem of the change of the scale parameter in the independent Gamma distribution.We use the reversible jump Markov chain Monte Carlo(RJMCMC)algorithm to compute the posterior distribution of the parameters and the location of the change points.Based on the RJMCMC algorithm,we analyzes the successive rising and falling rate.In chapter 1,we present a brief introduction of the derivation of change point;then we discuss the different expressions and common research methods of change point in different fields;In the end,the current research methods in single change point and multiple change point are mentioned.In chapter 2,Bayesian method is introduced.We describe what are the Gamma distribution and Gamma distribution family,and give some applications of the Gamma distribution in reality.At last,we give the assumption of the model and the prior distribution of some parameters.In chapter 3,we propose the RJMCMC algorithm based on Bayesian estimation,Monte Carlo method and M-H algorithm.Also,the steps of the RJMCMC algorithm are given,and the acceptance probability of four transformations based on RJMCMC algorithm for Gamma distribution is calculated.In chapter 4,a simulation example is designed to verify the correctness and efficiency of the RJMCMC method.We generate the Gamma distribution sequence with the change point and estimate the number of change-points used the RJMCMC algorithm,and compare it with the SN method.In chapter 5,we make an empirical analysis.We use the RJMCMC algorithm to the data from 2000 to 2015 and find out the change-points in the data.According to the position of the change-points,we find the change of the policies near the change-points and give the analysis.In chapter 6,we are taking a test statistic based on the least square method for the mean common breaks of panel data,and use the critical value of the test statistic simulated by Monte Carlo method to explore the existence and estimator of the mean common breaks of panel data.Finally,we analyze the daily return rate of six stock markets in Nasdaq,Nikkei,Hangseng.In chapter 7,there is a conclusion of this paper,at the same time,deficienciesand prospects are given.