| For many economic,financial and other data exhibit long range dependence and may contain change points,inference the change points in long memory time series become a popular topic in statistics.This paper proposes some methods to test the mean change point,variance change point and change in persistence in long memory time series,and evaluate their validity and feasibility via theoretical analysis,simulation and real data analysis.The details are as follows:The first chapter introduces the concept of change point and long memory time series,and lists the test methods in the literature about mean,variance and persist change point.Chapter 2 presents a new statistic to detect the mean change points that may exist in long memory time series.In order to facilitate the practical application,we present a Sieve Bootstrap procedure which can give asymptotic critical values of the statistic.Simulations indicate that the proposed methods can not only control the empirical size well but also improve the test power compared to the existing method.In the third chapter,we propose a method to test the variance change point in long memory time series,and a Sieve Bootstrap method which similar to that of Chapter 2 was constructed to approximate the critical values of the statistic.Simulations show that the proposed method performs well both for small to large and large to small variance change point in long memory time series.Further more,we illustrated our method by a set of ‘qing qing ke jiu' stock data.Chapter 4 proposes two modified statistics to test stationary to nonstationary persistent change point and nonstationary to stationary persistent change point in long memory time series respectively.Simulat-ations indicate that the proposed methods can not only control the empirical size well but also have satisfactory test power.Finally,we illustrate our tests by a set of a US inflation rate data.Chapter 5 concludes the paper and gives some prospects about the future research. |
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