Ratio detection for mean change in α mixing observations

A ratio test based on the indicators of the data minus the sample median is proposed to detect the change in the mean of α-mixing stochastic sequences. The asymptotic distribution of the test is derived under the null hypothesis. The consistency of the proposed test is also obtained under the hypothesis that μ changes at some unknown time. We also propose a consistent estimator for the change point on the ratio test. Simulations demonstrate that the test and the estimator behaves well for heavy-tailed sequences. At last, an empirical application demonstrate the validity of the test and the estimator.