Statistical Analysis On Mean Change Point Problems Of Long Memory Sequence And Its Application In Finance

In the past three decades,the problem of change points has been a research hotspot of scholars at home and abroad in statistics.In view of the long memory,characteristics of financial time series data,the use of long memory series to characterize its evolution has attracted extensive attention of scholars.In this thesis,we study the statistical analysis of mean change points based on long memory sequences.The main contents are as follows:The test of the mean change point of long memory sequences is studied.In the classical lo:ng memory mean point model,it is proved that the limit distribution of the clumulative statistic is a function of fractional Brownian motion under null hypothesis.At the same time,the consistency under alternative hypothesis is also obtained.The numerical simulation results show that the empirical size is close to the significance level without the mean change point.And the empirical power increases with the jump range of the mean change point and the sample size when there is a mean change point.In the non-stationary environment with variance change point,the test of the mean change point of long memory sequence is studied.The result shows that under the null hypothesis the asymptotic distribution of the CUSUM statistics is no longer standard,but closely related to the jump amplitude and appearance time of variance change points.At the same time,through further study of numerical simulation,it is found that the empirical size of statistics has a serious distortion phenomenon,that is,the greater the variation of the variance,the more backward the position of the variance change point,the more serious th,e distortion of the empirical size.Aiming at this defect,the Sparse Reconstruction Method and the Bootstrap Method is used to remove the influence of the variance change point on the test,and finally the robust test of mean change point is realized.By the empirical ana'lysis of two sets of financial time series data,the cotton price and agricultural bank stock price,the results show that the methods proposed in the thesis are effective for the test of mean change point.Therefor.studying the mean change points of long memory sequences has great theoretical significance for the statistical model of discontinuous conditions.