Persistence Variation Point Test

Since the last century20s,the research of changing point problems is a very popular topic in statistics.At present the changing point problems ont only have a wide variety of applications in industrial quality control field,but also have a large application background In the financial, economic, computer, medical science and other fields.In resent years,because the different method of data modeling arc due to the stability of the sequence in in the time scries analysis,testing of persistent changing point in nonlinear financial time series become to concern issues of many researchers.This paper studies two detection method of persistent changing point,one is a nonparamctric test based on sign function,the other one is a test based on unit root test.The first chapter, the research background of this paper and previous re-searches were introduced,and the main documents of detection methods of per-sistent changing point were summarized.Chapter two,the main background knowledge were introduced.Chapter three,a nonparametric test method based on sign function to test persistent change point was developed.We constructed a ratio statistic based on sign function.Under the null hypothesis, we proved the asymptotic normality of the statistic,and under the alternative hypothesis the consistency of the test is proved.Chapter four,a test method based on unit root test to test persistent change point was developed.We constructed a ratio statistie.Under the null hypothe-sis, we proved the asymptotic normality of the statistic,and under the alterna-tive hypothesis the consistency of the test is proved.At last, we sum up the conclusion of this paper.Also we point out the shortcomings of this paper and some unsolved problems in this research direction.