Analysis Of Parameter Change Point In The Fractional Integrated Autoregressive Moving Average Model

In practical applications,the short memory time series model is usually used to describe and predict objective processes.However,in recent years,itis found that many types of data,such as unemployment rate,GDP,exchange rate,radio and so on,have long memory characteristics,which is not suitable for the short memory model.Thefractional integrated autoregressive moving average model(ARFIMA)is a long memory model,which is widely used in the economic and financial fields.Due tothe effect of many factors,the long memory parameters of the model will change,that means,change point occurs.We studytesting,online-monitoring and estimationof the long memory parameter change point inARFIMA model.The first chapter introduces the concept of change point and SieveBootstrap,and gives the related research results of change point test,online-monitoring and change point estimation.The second chapterpresents a SieveBootstrap monitoring method to monitor the ARFIMA(p,d,q)model,and gives the SieveBootstrapmethod for approximating the critical value of the statistic.The simulation results show that the critical values determined by the SieveBootstrap method can not only control the empirical size well below the test level,but also have a good test power.Chapter 3 proposes a new statistic to test change point when parameter changes fromlarge to small for it can't be detected via the available method in the literature andthen uses the SieveBootstrap method to approximate the critical values.The simulation results show that new method has good behavior when parameter changes from large to small.In the fourth chapter,the CUSUM type estimators of the parameter change point are given,moreover,the consistency is proved and the convergence rate is derived.And it is analyzed the precisions of estimation by simulations at last.Chapter five presents the conclusion and some prospects of furtherresearch.