Change Point Detection In Long Memory Time Series Based On Two Types Of Bootstrap

Detecting change point in long memory time series is a popular topic in statistics in recent years,however,the most statistics have unstandard limiting distributions which lead their critical values can hardly to be determined.This thesis studies the effectiveness of Sieve Bootstrap and Block Bootstrap methods in approximating some change point test statistic in long memory time series,and want to find an optimal one for practical application.The main content is as follows:Investigate the advantages and disadvantages of Sieve AR Bootstrap,the fractional differenced Sieve Bootstrap and the fractional differenced Block Bootstrap methods in approximating the long memory time series,and the critical values of the selfnormalization ratio statistic which is designed to test its mean change point.Simulations show that the fractional differenced Sieve Bootstrap method has the best approximation in general and better than the direct simulation.Test unit root process to long memory process as well as long memory process to unit process change point via a ratio statistic.The limiting distribution of test statistic under the nonstationary long memory null hypothesis is derived.Moreover,we approximate the critical values of test statistic via the fractional differenced Sieve Bootstrap method.Simulation and empirical application illustrate the effectiveness and feasibility of proposed method.Study the mean change point detection problem in heavy tailed long memory time series based on the self-normalized ratio statistic and the Wilcoxon statistic.The fractional differenced Sieve Bootstrap method is also be used to approximate their critical values.Simulations indicates that the self-normalized ratio statistic only has some power for larger tail index,the Wilcoxon statistic,however,can significantly improve the test power in all tail index assumptions.Conclude the thesis and gives some research prospects.