The Research Of Change-Point Problem In Ma Model And Arma Model

This paper mainly studies the change-point problem in MA(q) model and ARMA(p,q) model.The first chapter is an introduction,the research significance and backgroung at home and abroad of change point problem was introduced in detail.The second chapter in the research of MA(q) change-point model,gives the displayed expressions of the change-point location and two stages of each parameter in two different situations,a situation is the coefficients of model were changed and the variance of the residual sequence was not changed,another situation is the coefficients of model were changed and the variance of the residual sequence was changed.Meanwhile,for instance to set the parameters of MA(2) change-point model,using the sample data obtained from the monte carlo simulation technique to test the accuracy of the likelihood ratio method applied in MA(q) change-point model.Then, In the third chapter.combine the research results in AR(p) change-point model based on likelihood ratio method with the work of the second chapter in this paper,get the parameter estimation results in ARMA(p,q) change-point model,and made a empirical test.Because under the situation of the model coefficients were not changed and the variance of the residual sequence was changed,it is hard to get the displayed expressions of the parameters in MA(q) change-point model.The change-point problem of MA(q) model in this kind of situation equivalent to the variance change-point problem of time series,can use SIC to distinguish.Therefore in the fourth chapter,set the parameters of MA(2) change-point model in the situation of the model coefficients were not changed and the variance of the residual sequence was changed, using the sample data obtained from the monte carlo simulation technique to test the accuracy of the SIC applied in this problem.The empirical results show that this idea is feasible.At last,In the fifth chapter,combine the likelihood ratio method and the SIC to distinguish the change-point of Chinese GDP time series.The result is Chinese GDP rate sequence after centralized existence of a variance change-point,at1977,and it is changed by model coefficients were changed and the variance of the residual sequence was changed.To get the two stages of development of Chinese GDP time series,mean1952-1977,1978-2012. After through further research shows that the modeling result of GDP time series in consideration of the change-point are superior to the model that did not consider the change-point situation.