Change Point Analysis And Application Of Trend Terms In Long Memory Time Series

Trend term change point as a kind of common points,related research achievements mainly consider is short memory time series model.Since many practical data have long memory,long memory time series trend change point has important theoretical value and practical significance.This paper studies the long memory time series trend change point test,on-line monitoring and estimation problem,specific content is as follows:First of all,based on the least squares fitting residual error to construct a new type CUSUM statistic to test the change point,in the absence of change point proved that the test statistic under the null hypothesis of limiting distribution is the functional type I fractional Brownian movement,under the alternative hypothesis proved the consistency of the test statistics,and puts forward with Sieve bootstrap method to determine the critical value of test statistics to avoid estimate the redundant parameters.Numerical simulation results show that the proposed new method can well control under the null hypothesis experience level,can achieve satisfactory experience under the alternative hypothesis.Secondly,based on the least squares fitting residual structure monitoring statistics online monitoring of long memory time series trend change point,proved that the monitoring statistic under the null hypothesis when there is no change the limit of the distribution and consistency under the alternative hypothesis,and construct the approximation threshold monitoring statistics of Sieve bootstrap method.Simulation results show that the proposed method can be a very well control experience level,experience a high potential and shorter average run length.Finally,CUSUM statistics,which is suitable for the estimation of mean change points,is used to study the estimation of change points of trend terms.simulation results show that this method can achieve good estimation effect only when the variation points are near the front,indicating that this method is not a consistent method for estimating change points of trend terms.