Based On Improved Ratio Statistic To Test Persistence Change Point With Heavy-tailed Sequences

Change point analysis is an important branch in time series and has broad application prospects.Because the persistence change point affects the stationarity of the sequence,and whether the sequence is stable or not determines the method of data modeling,it is particularly important to test whether there is a persistence change point in the sequences.Among the many test methods for persistence change point,the test based on ratio statistic is one of the research hotspots.Although the existing ratio statistic can test the persistence change point,its power is not ideal.Based on this,this paper tests the persistence change point of the heavy-tailed sequences on the basis of the improved ratio statistic.The specific research contents are as follows:Improve the ratio test of persistence change point with heavy-tailed sequences.Based on the existing ratio statistic,the corresponding improvement scheme is proposed,and the improved ratio statistic is used in the test model of persistence change point.The asymptotic distribution of the improved statistic under the null hypothesis is a functional of the Levy process,and the consistency of the test under the alternative hypothesis is proved.The numerical simulation shows that the size of the improved statistic fluctuates around the significance level,and the power has been significantly improved,which verifies the rationality and feasibility of the improved ratio statistic.Aiming at the defect that the asymptotic distribution of improved ratio statistic depends on the unknown heavy-tailed index,the Subsampling test,Bootstrap test and Block bootstrap test are proposed to approximate the critical value of the test statistic,so as to complete the robust test of the persistence change point of the heavy-tailed sequences.Under the null hypothesis,it is proved that the distribution functions of the three test statistics converge to the distribution function of the original statistic according to the probability.The simulation results show that the three test methods proposed can effectively control the size and power,and the power is sensitive to factors such as sample size,heavy-tailed index and change point position:the sample size larger,the power larger;the heavy-tailed index becomes smaller,and the power becomes smaller;the higher the position of the change point,the greater the power,which demonstrates the effectiveness of the proposed test methods.