The CUSUM statistics of change-point models based on dependent sequences

Abstract

In this paper, we investigate the mean change-point models based on associated sequences. Under some weak conditions, we obtain a limit distribution of CUSUM statistic which can be used to judge the mean change-mount ${\delta }_n$ is satisfied or dissatisfied $n^{1/2}{\delta }_n=o\left(1\right)$. We also study the consistency of sample covariances and change-point location statistics. Based on Normality and Lognormality data, some simulations such as empirical sizes, empirical powers and convergence are presented to test our results. As an important application, we use CUSUM statistics to do the mean change-point analysis for a financial series.

Keywords:

• CUSUM statistics
• limit distribution
• change-points
• associated sequences
• convergence rate

MSC (2010):

• 62F12

Acknowledgments

The authors are deeply grateful to editors and anonymous referees for their careful reading and insightful comments. The comments led us to significantly improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work is supported by NNSF of China (11701004, 11801003, 12001105), NSF of Anhui Province (2008085MA14, 1808085QA03, 1808085QA17), the PSF of China (2019M660156) and PNSRP of Anhui Colleges (KJ2019A0006, KJ2019A0021).