Based Ratio Test To Detect The Stable Index Change Point Under Infinite Variance Sequence.

Change point analysis is a hot issuc in statistics in the past two decades,and has broad prospccrs in nmany fields Studies have shown that financial datl can no longer be described by traditionat Gaussian sequences because they lend to have spikes and heavy tails.In particlar.with the continuous development of the sophisticated quantitative requirements for the analysis of the tail features of financial data in modem emerging disciplines,the use of the heavy-tailed distribution stable index to characterize the tail-thickness of time-series data to achiceve the purpose.of measuring financial risk.Therefore,this thesis focuses on the problem of the infinite variance sequence stable index change point.The specific contents are as follows:In the environment without mean change points,the ratio type statistic is used to detect the infinite variance sequence stable index change point.Under the appropriate pre-conditions,the asymptotic distribution of the suatistic under the null hypothesis is obtained.and its consistency the alternative hypothesis is proved Aiming at the defect that the asymptotic distritbution depends on the unknown stable index,two methods of bootstrap test and polynomial fitting arc proposed to determine the critical value of the limit distribution,and finally the lest of the stable index change point is realized.The numerical simulation shows that the test power of the statistic is sensitive to the sudd,en change,such as the stable index change point and the jump range,which indicates the fesibility and effectiveness of the method in the thesis to test the stable index change point.In the environment with mean change points,the limit properties of the stable index test for the infinite variance sequence are discussed based on the ratio statistic.The study found that the asymptotic distribution of statistics is consistent with the asymptotic distribution in a stationary environment.both of which are levy process functionals.However,the numerical simulation shows that the statistical lest size level is seriously distorted,especially when the jump range of mean change point is larger or the change point is closer to the back of the sample,the more serious distortion is detected.Aiming at this deficiency,a sparse reconstruction method is proposed to eliminate the influence of the mean change point on the test statistic,and to achieve a robust test of the stable index change point.The feasibility and effectiveness of this method are verified by numerical simulation.