Ratio Tests For Persistence Change With Heavy Tail Series

Change point problems,as one of the core areas of research in statistics,have been a hot topic for domestic and foreign scholars.During the past two decades,there is a growing body of evidence to suggest that economic and financial time series display changes in persistence.And heavy tail series can better describe the characteristic of aiguille and long tail in the financial data.Therefore,it is especially important to study on persistence change with heavy tail series.In chapter 2,we propose a truncated test which is based on the fact that the power is lower under the alternative hypothesis with a persistence change point when the heavy tail index ? is smaller.After the original data is truncated,the power is effectively improved,and the uniform estimation of the persistence change point is given due to the need of the truncation processing.It is found that after the truncation,the heavy tail series is transformed from the infinite variance to the finite variance,and the limit distribution of the statistics of the truncated test is same with the case of Gaussian series,in other words,the distribution of the truncated statistics is not connected with the characteristic index ,so that the detection also has a good effect in the case of the heavy tail index is small.Through the simulation found that the truncated test is no obvious advantage under the null hypothesis,but it is effective to improve the power under the alternative hypothesis.In chapter 3,we consider the effect of persistence change test when the series exist an index change point at the moment.We obtained conclusions as follows: under the null hypothesis that the circumstance of the series only existed an index change point,if the heavy tail index change from large to small,the statistics is diverging at a speed of 2/2-2/1,and the larger of the 2-1 is,the faster the divergence is.If the index change from small to large,the statistics converges to the bounded constant.But the numerical simulation shows that no matter how the change of will lead to the size distortions,and the size distortions shows more serious when 1> 2.Under the alternative hypothesis,the series have persistence change point and index change point,in the case of 1> 2,the power is increased which makes it easier to reject the null hypothesis.But the power will loss when k₁? k₂.