Testing Change Point In The Dependent Observations

To study the problem of change points is a hot topic in Statistics.There are many theoretical results on the case of independent sequences.In this paper,we focus on the detection of the change point in the mean of heavy-tailed dependent observations and in the variance of dependent observations.For the mean change point in the heavy-tailed observa-tions,a residual-based block bootstrap method is proposed to approximate the asymptotic null distribution,rather than conventional i.i.d bootstrapThis paper is divided into five parts.The first part is an introduction which introduces the research background of the change point problem briefly and innovation.In the second part,we give the model,statistics and the asymptotic distribution of the statistic,the block bootstrap procedure is proposed and the reasonability is proved.In the third part,we give the model and statistic to detect variance change point in linear process and linear process with long memory.In the fourth part,we use the Monte Carlo method to simulate and show the empirical size and power of the statistics.In addition,stock price is introduced to demonstrate the validity which mentioned in this paper.In the fifth part,we summarize the contents of the paper and introduce the outlook.