The Statistical Analysis For Gradual Changes In The Mean Of Two Models

The change-point analysis has been regarded as an important part of researches in statistics,which can be divided into the abrupt changes and the gradual changes according to the different forms of the change point.In meteorology,hydrology and other fields,the distribution of some meteorological elements have long-range dependence,and may change gradually from an unknown moment.In order to research the changes in meteorological elements,it is necessary to test and estimate the gradual change time,which makes the study of gradual changes in long memory processes attract more and more scholars' attention.At the same time,in the financial market,the financial asset return has characteristics of “peak” and “heavy-tail”,and financial time series exist change-point problems,which makes analysis of gradual changes in heavy-tailed processes become a hotspot of statistical research.This thesis considers the gradual changes in two classes of mean models,where one class is heavy-tailed mean model;the other is long memory mean model.The research contents of the thesis are as follows:Firstly,estimation on gradual change point in the mean model with random error is ARCH process is studied.Least squares method is constructed and the consistency of the estimator is proved.The rate of convergence is also studied.Numerical simulations are used to test the influence of model parameter change and location of change point change on estimators,the results demonstrate that the proposed method is effective.Next,the single change point test on the mean of long memory gradual change model is considered.Under the appropriate assumptions,Ratio test method is constructed and both the limit distribution of the test statistic under the null hypothesis and the alternative hypothesis are derived.The consistency of the test is also proved.The influence of longmemory parameter change and model parameter change on the empirical size and empirical power of the test is verified by numerical simulation.And the simulation results are compared with the results of CUSUM test.Finally,the results from real data analysis support the argument.