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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, China

    Zhanshou Chen

  2. Academy of Plateau Science and Sustainability, Xining, 810008, China

    Zhanshou Chen

  3. Department of Applied Mathematics, Xi’an University of Technology, Xi’an, 710048, China

    Fuxiao Li

  4. College of Finance, Xingjiang University of Finance and Economics, Urumqi, 830012, China

    Li Zhu

  5. School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, China

    Yuhong Xing

  6. Academy of Plateau Science and Sustainability, Xining, 810008, China

    Yuhong Xing

Authors
  1. Zhanshou Chen
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  2. Fuxiao Li
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  3. Li Zhu
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  4. Yuhong Xing
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Corresponding author

Correspondence to Zhanshou Chen.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11661067, 11801438, 71661028, 61966030, the Natural Science Foundation of Qinghai Province under Grant No. 2019-ZJ-920.

This paper was recommended for publication by Editor ZHANG Xinyu.

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Chen, Z., Li, F., Zhu, L. et al. Monitoring Mean and Variance Change-Points in Long-Memory Time Series. J Syst Sci Complex 35, 1009–1029 (2022). https://doi.org/10.1007/s11424-021-0222-1

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  • DOI: https://doi.org/10.1007/s11424-021-0222-1

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