Study On Two Kinds Of Change Point Problems Of Long Memory Sequence

Change point problems in the field of statistics has been one of the hot issues of domestic and foreign scholars. With the rapid development and continuous diversification of economic, the presence of structural changes in the financial time series appear more frequent. At the same time, more and more financial data which show characteristics of long memory series, which can no longer be describe by the common normal distribution. In view of this, the study on the change point of long memory sequence has a very important significance. The innovation of the paper is the more systematic study on the combination of change point and long memory sequences on the basis of existing research ways of change point.The first class of the change point of long memory sequence has established two long memory series with mean change point and trend change point. There are a number of analysis of spurious regression based on t- test statistic. The results of research show that, the t- test statistics of the data model of two kinds of existing change points are divergent at the speed of (1/2) which has led the spurious. In order to verify the correctness of asymptotic distribution of t- test statistic it has made a sensitivity study in the factors by numerical simulation Monte Carlo. Experimental results show that, regardless of the time of change points is the same as long as there are structure transformation point, the rejection rate of t- test statistic will increase with the increasing sample size which with lead the spurious regression. And compared with the long memory sequence contain mean change points, the trend change points generate the spurious regression easily. The spurious regression not only has connection with the time of change points of the long memory sequence, but also be sensitive with the long memory index.The second category of the change point of long memory sequence has considered the problem of the change points of long memory index, and the problem of the change points of regression function at non-parametric regression model. Given the test statistic and the estimator of change point in the part of change point of regression function. They are both based on kernel estimation of local linear regression function. Derived the asymptotic distribution of the test statistic. and proved the consistency of the test and estimation. In addition, the consistency of test and estimation is proved. By Monte Carlo simulation, the Bootstrap test method is used to calculate the size and power. In the part of change point of long memory index, the CUSUM test statistic is constructed based on the square of the residual series, and its asymptotic distribution is derived. At the same time, under certain conditions, it's proved that the test statistic converges to the upper bound of the Brown bridge. By numerical simulation, it has got the size and power and the estimate of change point,under the alternative hypothesis. Results of the numerical simulation show the method provided by the paper has a good effect on the detection and estimation of the change points regression function and the change points of long memory index.