Ratio detection for mean change in α mixing observations

ABSTRACT

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.

KEYWORDS:

• Consistence
• change point
• estimator
• median
• ratio test.

MATHEMATICS SUBJECT CLASSIFICATION:

• primary 62G08
• 62M10

Acknowledgments

Financial support from this work is supported by the National Natural Science Foundation of China (No. 11226217, 71501115), Natural Science Foundation for Youths of Shanxi Province (No. 201701D221003), Research Project Supported by Shanxi Scholarship Council of China (2016-015) and the Postdoctoral Science Foundation and the Postdoctoral Science Special Foundation of China (No. 2012M510772, 2013T60266) are gratefully acknowledged. Liu’s work is supported by the Humanity and Social Science Foundation of Ministry of Education of China (No. 14YJA790034) and the National Social Science Foundation of China (No. 15BJY164).