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A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters

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  • Holger Dette
  • Josua Gösmann

Abstract

In this article, we propose a new approach for sequential monitoring of a general class of parameters of a d-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a closed-end method, which is motivated by the likelihood ratio test principle and compare the new method with two alternative procedures. We also incorporate self-normalization such that estimation of the long-run variance is not necessary. We prove that for a large class of testing problems the new detection scheme has asymptotic level α and is consistent. The asymptotic theory is illustrated for the important cases of monitoring a change in the mean, variance, and correlation. By means of a simulation study it is demonstrated that the new test performs better than the currently available procedures for these problems. Finally, the methodology is illustrated by a small data example investigating index prices from the dot-com bubble. Supplementary materials for this article are available online.

Suggested Citation

  • Holger Dette & Josua Gösmann, 2020. "A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1361-1377, July.
    • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:531:p:1361-1377
    DOI: 10.1080/01621459.2019.1630562
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    Cited by:

    1. Zifeng Zhao & Feiyu Jiang & Xiaofeng Shao, 2022. "Segmenting time series via self‐normalisation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1699-1725, November.
    2. Haoran Lu & Dianpeng Wang, 2024. "Grouped Change-Points Detection and Estimation in Panel Data," Mathematics, MDPI, vol. 12(5), pages 1-20, March.
    3. Castrillón-Candás, Julio E. & Kon, Mark, 2022. "Anomaly detection: A functional analysis perspective," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Mikkel Bennedsen, 2021. "Designing a statistical procedure for monitoring global carbon dioxide emissions," Climatic Change, Springer, vol. 166(3), pages 1-19, June.
    5. Lazar, Emese & Wang, Shixuan & Xue, Xiaohan, 2023. "Loss function-based change point detection in risk measures," European Journal of Operational Research, Elsevier, vol. 310(1), pages 415-431.

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