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Detecting multiple generalized change-points by isolating single ones

Author

Listed:
  • Andreas Anastasiou

    (University of Cyprus)

  • Piotr Fryzlewicz

    (The London School of Economics and Political Science)

Abstract

We introduce a new approach, called Isolate-Detect (ID), for the consistent estimation of the number and location of multiple generalized change-points in noisy data sequences. Examples of signal changes that ID can deal with are changes in the mean of a piecewise-constant signal and changes, continuous or not, in the linear trend. The number of change-points can increase with the sample size. Our method is based on an isolation technique, which prevents the consideration of intervals that contain more than one change-point. This isolation enhances ID’s accuracy as it allows for detection in the presence of frequent changes of possibly small magnitudes. In ID, model selection is carried out via thresholding, or an information criterion, or SDLL, or a hybrid involving the former two. The hybrid model selection leads to a general method with very good practical performance and minimal parameter choice. In the scenarios tested, ID is at least as accurate as the state-of-the-art methods; most of the times it outperforms them. ID is implemented in the R packages IDetect and breakfast, available from CRAN.

Suggested Citation

  • Andreas Anastasiou & Piotr Fryzlewicz, 2022. "Detecting multiple generalized change-points by isolating single ones," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 141-174, February.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:2:d:10.1007_s00184-021-00821-6
    DOI: 10.1007/s00184-021-00821-6
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    References listed on IDEAS

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    1. 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.
    2. Holger Dette & Theresa Eckle & Mathias Vetter, 2020. "Multiscale change point detection for dependent data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1243-1274, December.
    3. Ross, Gordon J., 2015. "Parametric and Nonparametric Sequential Change Detection in R: The cpm Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(i03).
    4. Fryzlewicz, Piotr, 2020. "Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection—rejoinder," LSE Research Online Documents on Economics 106681, London School of Economics and Political Science, LSE Library.
    5. Fryzlewicz, Piotr, 2020. "Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection," LSE Research Online Documents on Economics 103430, London School of Economics and Political Science, LSE Library.
    6. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    7. Rafal Baranowski & Yining Chen & Piotr Fryzlewicz, 2019. "Narrowest‐over‐threshold detection of multiple change points and change‐point‐like features," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 649-672, July.
    8. 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.
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    Cited by:

    1. Maeng, Hyeyoung & Fryzlewicz, Piotr, 2023. "Detecting linear trend changes in data sequences," LSE Research Online Documents on Economics 119280, London School of Economics and Political Science, LSE Library.

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