| From the 1920s,the problem of persistence change test has attracted wide attention in the field of Statistics.It is very important to find some ways to solve the problem of heavy-tailed series that many financial time series have the characteristic of a heavier tail than the normal variable.In fact,the stable index ? is often unknown and complication procedure is usually involved in estimating it.In order to determine the critical values of the statistic,we need an approximation method.In this paper,three sampling methods are compared and the Monte Carlo simulation shows the performances of empirical levels and powers under different methods.Finally,we indicate the validity of block bootstrap method that using the exchange rate between RMB and U.S.dollars from May 1 to December 31 of 2009.This paper is divided into six parts.The first part is an introduction which introduces the research background of the per-sistence change problem briefly and innovation.In the second part,we give the model and statistic and calculate the asymptotic distri-bution of the statistic.In the third part,we give the sampling process of i.i.d bootstrap method,subsampling method and block bootstrap method and prove the rationality of the three methods.In the fourth part,we use the Monte Carlo method to study the sampling methods mentioned in this paper and the tables show the performances of the empirical level and power under different methods.In addition,we summarize the performances of the sampling methods for the analysis of the problem of the persistence change point test of the heavy tailed series which mentioned in this paper and analyze the reasons of the different performances.In the fifth part,we introduce importance of study exchange rate briefly and use the exchange rate between RMB and U.S.dollars from May 1 to December 32 of 2009 to indicate the validity which mentioned in this paper.In the sixth part,we summarize the contents of the paper and introduce the outlook. |
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