Statistical Analysis Of The Change Point Test For The Persistence Of Heavy Tailed Sequences

Study on the change point problem was first applied in the field of industrial quality control.At present,It is not only in the field of industrial quality control,but also in the fields of economy,finance,medicine,computer,network security,signal tracking and so on has a lot of applications.In recent years,since the problem of persistent change has important application in practice,the problem of persistent change has been paid close attention by economists,but many financial-related time series are showing a sharp and thick tail,Therefore,it is very important to study the persistence point of the heavy-tailed sequence.In this paper,two methods for the determination of the persistence of the heavy-tailed sequence are given.The first is that the residual ratio test of the hypothesis that the original hypothesis is a unit process and the alternative hypothesis is a stable process to a unit root process.The second method study change point test of wild bootstrap under the hypothesis that the original hypothesis is a stable process and the alternative hypothesis is a stable process to a unit root process.Through the numerical simulation to obtain their own experience level and empirical potential function value.The paper consists of five parts.The first chapter is the introduction,which describes the change point problem,and briefly introduces some representative methods of change point test:Maximum likelihood method,Least square method,Cumulative sum method,Empirical Quotations method.The second chapter is the basic theory of knowledge.This chapter introduces some of the background knowledge related to this article.In the third chapter,we discuss the ratio test of heavy tailed persistence.In this chapter,we study ratio test that the original hypothesis is the unit root process,and the alternative is assumed to be the stabilization process,and gives its asymptotic distribution under null hypothesis and alternative hypothesis.The convergence rate is obtained under alternative hypothesis.By means of numerical simulation,the empirical and potential function values are obtained.The fourth chapter is based on the Wild bootstrap heavy tailed persistence change point test.In this chapter,we mainly study the residual ratio test of the hypothesis that the original hypothesis is a stable process and the alternative hypothesis is a stable process to a unit root process.Then,the Wild bootstrap algorithm is used to sample them,and the asymptotic distribution of them is found to be consistent.The empirical and potential function values are obtained by numerical simulation.The fifth chapter is the conclusion,which summarizes the main content of this paper.