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 Auto-Regressive Moving Average Processes and Generalized Auto-Regressive Conditional Heteroscedasticity Processes 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 sequential analysis for detecting changes named cumulative sum 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 has a better performance in comparison to Berkes et al. (2009 Berkes, I., Gombay, E., Horvath, L. (2009). Testing for changes in the covariance structure of linear processes. J. Stat. Plan. Inf. 139:2044–2063.[Crossref], [Web of Science ®] , [Google Scholar]).