Estimation And Test Of Two Kinds Of Heavy-tail Dependent Sequence Change Points

The statistical analysis of time series has always been the focus of attention.In recent years,with the rapid development of computer technology,the research on time series has entered a new stage.The research and discussion on the change point problem in time series is also more and more in-depth.Heavy-tail dependence series is a common time series in financial markets.In this paper,we mainly study the problem of change point test in Heavy-tail dependent series.The main contents of the study are as follows:In this paper,the mean change points of thick-tail sequences are estimated,the cumulative sum form estimates are given,and the asymptotic behavior of the estimators is discussed.The Ratio test method is used to study the single change point of the mean of Heavy-tail dependent sequence.The statistic is defined based on the ratio of the cumulative sum function,in the appropriate hypothetical conditions,the limit distribution of the test statistic is given under the original assumption.On this basis,the consistency test of the defined statistics is deduced and it is proved that the test statistics have effectiveness.Using Ratio method to test GARCH model mean change point problems,construct Ratio statistics,deduce and prove the consistency test of statistics.Finally,through numerical simulation and stock data analysis of IBM stock from 2018 to2019,it is proved that this method is effective for GARCH model.