Monitoring Mean and Variance Change-Points in Long-Memory Time Series

doi:10.1007/s11424-021-0222-1

Journal of Systems Science and Complexity ›› 2022, Vol. 35 ›› Issue (3): 1009-1029.DOI: 10.1007/s11424-021-0222-1

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Monitoring Mean and Variance Change-Points in Long-Memory Time Series

CHEN Zhanshou^1,2, LI Fuxiao³, ZHU Li⁴, XING Yuhong^1,2

1. School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, China; 2. Academy of Plateau Science and Sustainability, Xining 810008, China; 3. Department of Applied Mathematics, Xi'an University of Technology, Xi'an 710048, China; 4. College of Finance, Xingjiang University of Finance and Economics, Urumqi 830012, China 6. Academy of Plateau Science and Sustainability, Xining 810008, China

Received:2020-09-14 Revised:2020-12-28 Online:2022-06-25 Published:2022-06-20
Supported by:
This research was supported by the Natural Science Foundation of Heilongjiang Province under Grant No. LH2020F035.

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CHEN Zhanshou, LI Fuxiao, ZHU Li, XING Yuhong. Monitoring Mean and Variance Change-Points in Long-Memory Time Series[J]. Journal of Systems Science and Complexity, 2022, 35(3): 1009-1029.

This paper proposes two ratio-type statistics to sequentially detect mean and variance change-points in the long-memory time series. The limiting distributions of monitoring statistics under the no change-point null hypothesis, alternative hypothesis as well as change-point misspecified hypothesis are proved. In particular, a sieve bootstrap approximation method is proposed to determine the critical values. Simulations indicate that the new monitoring procedures have better finite sample performance than the available off-line tests when the change-point nears to the beginning time of monitoring, and can discriminate between mean and variance change-point. Finally, the authors illustrate their procedures via two real data sets:A set of annual volume of discharge data of the Nile river, and a set of monthly temperature data of northern hemisphere. The authors find a new variance change-point in the latter data.

Key words: Change-point monitoring, long-memory time series, ratio-type statistic, sieve bootstrap

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