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Bivariate change point detection: Joint detection of changes in expectation and variance

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  • Michael Messer

Abstract

A method for change point detection is proposed. We consider a univariate sequence of independent random variables with piecewise constant expectation and variance, apart from which the distribution may vary periodically. We aim to detect change points in both expectation and variance. For that, we propose a statistical test for the null hypothesis of no change points and an algorithm for change point detection. Both are based on a bivariate moving sum approach that jointly evaluates the mean and the empirical variance. The joint consideration helps improve inference compared with separate univariate approaches. We infer on the strength and the type of changes with confidence. Nonparametric methodology supports the analysis of diverse data. Additionally, a multiscale approach addresses complex patterns in change points and effects. We demonstrate the performance through theoretical results and simulation studies. A companion R‐package jcp (available on CRAN) is discussed.

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  • Michael Messer, 2022. "Bivariate change point detection: Joint detection of changes in expectation and variance," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 886-916, June.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:2:p:886-916
    DOI: 10.1111/sjos.12547
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    1. Kuelbs, J., 1973. "The invariance principle for Banach space valued random variables," Journal of Multivariate Analysis, Elsevier, vol. 3(2), pages 161-172, June.
    2. Klaus Frick & Axel Munk & Hannes Sieling, 2014. "Multiscale change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 495-580, June.
    3. Zhenguo Gao & Zuofeng Shang & Pang Du & John L. Robertson, 2019. "Variance Change Point Detection Under a Smoothly-Changing Mean Trend with Application to Liver Procurement," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 773-781, April.
    4. Carina Gerstenberger & Daniel Vogel & Martin Wendler, 2020. "Tests for Scale Changes Based on Pairwise Differences," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1336-1348, July.
    5. Fan Wu & Su Zhao & Bin Yu & Yan-Mei Chen & Wen Wang & Zhi-Gang Song & Yi Hu & Zhao-Wu Tao & Jun-Hua Tian & Yuan-Yuan Pei & Ming-Li Yuan & Yu-Ling Zhang & Fa-Hui Dai & Yi Liu & Qi-Min Wang & Jiao-Jiao , 2020. "Author Correction: A new coronavirus associated with human respiratory disease in China," Nature, Nature, vol. 580(7803), pages 7-7, April.
    6. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    7. Lindgren, Georg, 1980. "Point processes of exits by bivariate Gaussian processes and extremal theory for the [chi]2-process and its concomitants," Journal of Multivariate Analysis, Elsevier, vol. 10(2), pages 181-206, June.
    8. Florian Pein & Hannes Sieling & Axel Munk, 2017. "Heterogeneous change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1207-1227, September.
    9. D. A. Hsu, 1977. "Tests for Variance Shift at an Unknown Time Point," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(3), pages 279-284, November.
    10. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    11. Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
    12. Holmes, Mark & Kojadinovic, Ivan & Quessy, Jean-François, 2013. "Nonparametric tests for change-point detection à la Gombay and Horváth," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 16-32.
    13. Fan Wu & Su Zhao & Bin Yu & Yan-Mei Chen & Wen Wang & Zhi-Gang Song & Yi Hu & Zhao-Wu Tao & Jun-Hua Tian & Yuan-Yuan Pei & Ming-Li Yuan & Yu-Ling Zhang & Fa-Hui Dai & Yi Liu & Qi-Min Wang & Jiao-Jiao , 2020. "A new coronavirus associated with human respiratory disease in China," Nature, Nature, vol. 579(7798), pages 265-269, March.
    14. Stefan Albert & Michael Messer & Julia Schiemann & Jochen Roeper & Gaby Schneider, 2017. "Multi-Scale Detection of Variance Changes in Renewal Processes in the Presence of Rate Change Points," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 1028-1052, November.
    15. Zeileis, Achim & Shah, Ajay & Patnaik, Ila, 2010. "Testing, monitoring, and dating structural changes in exchange rate regimes," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1696-1706, June.
    16. David S. Matteson & Nicholas A. James, 2014. "A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 334-345, March.
    17. Górecki, Tomasz & Horváth, Lajos & Kokoszka, Piotr, 2018. "Change point detection in heteroscedastic time series," Econometrics and Statistics, Elsevier, vol. 7(C), pages 63-88.
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    1. Hu, Qirui, 2024. "Change point analysis of functional variance function with stationary error," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

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