Change-point Analysis And Parameters Estimation In AR(p) Models

Ever since 1980 s,change-point problem has been hot issue in statistical studies.Not only for its profound theoretical values,but it has also been widely used in quality control,finance,economics,medical science and computer science.Our main work in this paper is as follows:First,maximum likelihood method and conditional least square method are used to analyze the change-point problem.In situation that the data matrix is not full-rank,Moore-Penrose inverse matrix is used to give a unified expression of the model parameters' MLE and the estimator of change-point location.With conditional least square method a U_k statistic is introduced and the distribution of the U_k is a beta distribution.By calculating the beta distribution's quantile and the value of the U_k statistic,we got a new T_k statistic to estimate the location of the change-point.The new estimator is calculation easy.Second,we introduce Bayesian method to study the change-point problem of AR(p)models.Assuming that the prior distribution of the auto-regression coefficients is multivariate normal distribution and the prior distribution of the variance is inverse gamma distribution,we discussed the change-point problem in AR(p)models under situations of both variance changed and unchanged.An explicit expression of the change-point location estimation and Bayesian estimation of parameters is given.At last we apply our new least square method to some simulation data and effect is ideal.More applications of the method are done in SSE Composite Index data and some data in flight tests of an aircraft and both the applications are successful for the change-point we estimated are in accordance with the data shift.