Testing For Change Points Based On The Invariance Principles In Time Series

In this thesis, we begin with that how to test a change point in mean, the common CUSUM statistic, Kolmogorov-Smirnov test statistic involve a consistent long run vari-ance estimator,but the statistic based on the SN method in Shao, Zhang(2012) avoid the problem.We expand the test statistic based on the SN method to test more than one change point in a general framework, then we give the distribution of our statistic under the null hypothesis and proof it.After a detailed discussion on the method, we presented our statistics in the test of the change points in covariance and the coefficient of AR (1) model, to illustrate the application of the test statistics.