Statistical Inference Of Multiple Change Points In AR(1) Model

The change point problem in autoregressive model has always been one of the hot topics concerned by scholars,and it has been widely used in industrial production,financial market,quality control and many other fields.In this thesis,the AR(1)model with a change point proposed by Kejriwal and Perron(2012)is improved and extended to the general multiple change points case.Firstly,for the AR(1)model with a change point,Kejriwal and Perron(2012)have given the estimator and convergence of single change point in I(1)-I(0)process.On this basis,this paper further considers the estimation of a change point inI(0)-I(1)process.Through the least square estimation,this thesis obtains the change point estimator in the case of I(0)-I(1),and proves its convergence and convergence speed.At the same time,the reliability of the theoretical results is verified by numerical simulation.This result is symmetrical with that in Kejriwal and Perron(2012).Secondly,this thesis extends the results of Kejriwal and Perron(2012)to the case of multiple change points.For the AR(1)model with two change points,I(0)-I(1)-I(0)and I(1)-I(0)-I(1)are considered respectively.Through the least square estimation,this thesis gives the estimator of change points in the process of I(0)-I(1)-I(0),and proves the convergence and convergence rate of the estimator.At the same time,it is proved theoretically that the least square estimator of change point does not exist in the process of I(1)-I(0)-I(1).On this basis,this thesis gives the conditions for the existence of the least squares estimator of the change points in the general AR(1)model with n(n≥3)change points.In conclusion,this thesis studies the statistical inference of multiple change points in general AR(1)model.Based on the work of Kejriwal and Perron(2012),this thesis improves the least square estimation method of change points,and extends it to the general AR(1)model of change points.At the same time,it theoretically proves the existence conditions of the least square estimation of change points and the convergence of the estimator.