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 alpha-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 mu 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.