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

Saisai Ding; Hongyan Fang; Xiang Dong; Wenzhi Yang

doi:10.1080/02664763.2021.1913104

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

J Appl Stat. 2021 Apr 12;49(10):2593-2611. doi: 10.1080/02664763.2021.1913104. eCollection 2022.

Authors

Saisai Ding¹, Hongyan Fang¹, Xiang Dong², Wenzhi Yang¹

Affiliations

¹ School of Mathematical Sciences, Anhui University, Hefei, People's Republic of China.
² School of Life Sciences, Anhui University, Hefei, People's Republic of China.

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 $δ_{n}$ is satisfied or dissatisfied $n^{1 / 2} δ_{n} = o (1)$ . 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: 62F12; CUSUM statistics; associated sequences; change-points; convergence rate; limit distribution.

Grants and 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).