The CUSUM test for detecting structural changes in strong mixing processes

Strong mixing property holds for a broad class of linear and nonlinear time series models such as ARMA and GARCH models. In this article we study correlation structure of strong mixing sequences, and some asymptotic properties are presented. We also present a new method for detecting change point in correlation structure of strong mixing sequences, and present a nonparametric CUSUM test statistic for this. Asymptotic consistency of this test statistics is shown. This method is applied to simulated data of some linear and nonlinear models and power of the test is evaluated. For linear models, it is shown that this method have a better performance in compare to Berkes et al.(2009).