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Unsupervised Self-Normalized Change-Point Testing for Time Series

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  • Ting Zhang
  • Liliya Lavitas

Abstract

We propose a new self-normalized method for testing change points in the time series setting. Self-normalization has been celebrated for its ability to avoid direct estimation of the nuisance asymptotic variance and its flexibility of being generalized to handle quantities other than the mean. However, it was developed and mainly studied for constructing confidence intervals for quantities associated with a stationary time series, and its adaptation to change-point testing can be nontrivial as direct implementation can lead to tests with nonmonotonic power. Compared with existing results on using self-normalization in this direction, the current article proposes a new self-normalized change-point test that does not require prespecifying the number of total change points and is thus unsupervised. In addition, we propose a new contrast-based approach in generalizing self-normalized statistics to handle quantities other than the mean, which is specifically tailored for change-point testing. Monte Carlo simulations are presented to illustrate the finite-sample performance of the proposed method. Supplementary materials for this article are available online.

Suggested Citation

  • Ting Zhang & Liliya Lavitas, 2018. "Unsupervised Self-Normalized Change-Point Testing for Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 637-648, April.
    • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:522:p:637-648
    DOI: 10.1080/01621459.2016.1270214
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    Citations

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    Cited by:

    1. Jiang, Feiyu & Zhao, Zifeng & Shao, Xiaofeng, 2023. "Time series analysis of COVID-19 infection curve: A change-point perspective," Journal of Econometrics, Elsevier, vol. 232(1), pages 1-17.
    2. Y Hoga, 2018. "A structural break test for extremal dependence in β-mixing random vectors," Biometrika, Biometrika Trust, vol. 105(3), pages 627-643.
    3. Casini, Alessandro, 2023. "Theory of evolutionary spectra for heteroskedasticity and autocorrelation robust inference in possibly misspecified and nonstationary models," Journal of Econometrics, Elsevier, vol. 235(2), pages 372-392.
    4. Yannick Hoga, 2024. "Persistence-Robust Break Detection in Predictive Quantile and CoVaR Regressions," Papers 2410.05861, arXiv.org.
    5. Hong, Yongmiao & Linton, Oliver & McCabe, Brendan & Sun, Jiajing & Wang, Shouyang, 2024. "Kolmogorov–Smirnov type testing for structural breaks: A new adjusted-range based self-normalization approach," Journal of Econometrics, Elsevier, vol. 238(2).
    6. 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.
    7. Liu, Bin & Zhang, Xinsheng & Liu, Yufeng, 2022. "High dimensional change point inference: Recent developments and extensions," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    8. Christis Katsouris, 2023. "Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models," Papers 2308.13915, arXiv.org.
    9. Castrillón-Candás, Julio E. & Kon, Mark, 2022. "Anomaly detection: A functional analysis perspective," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    10. Qing Yang & Yu-Ning Li & Yi Zhang, 2020. "Change point detection for nonparametric regression under strongly mixing process," Statistical Papers, Springer, vol. 61(4), pages 1465-1506, August.
    11. Michal Pešta & Martin Wendler, 2020. "Nuisance-parameter-free changepoint detection in non-stationary series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 379-408, June.

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