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This paper presents two new simple statistic respectively to detect the long memory time series of the changes from smooth to non-stationary and persistence in smooth change from nonstationary variation point, two statistics under the null hypothesis is given the limits of the distribution, and proves that under the alternative hypothesis testing method. The consistency of the data simulation results show that the proposed method not only can good control inspection level, and has high potential test. At last, by a group of us inflation data to illustrate the practicability of this method.

Test and Application of Persistence Point of Long Memory Time Series