IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v74y2022i4d10.1007_s10463-021-00811-5.html
   My bibliography  Save this article

Two-stage data segmentation permitting multiscale change points, heavy tails and dependence

Author

Listed:
  • Haeran Cho

    (University of Bristol)

  • Claudia Kirch

    (Otto-von-Guericke University)

Abstract

The segmentation of a time series into piecewise stationary segments is an important problem both in time series analysis and signal processing. In the presence of multiscale change points with both large jumps over short intervals and small jumps over long intervals, multiscale methods achieve good adaptivity but require a model selection step for removing false positives and duplicate estimators. We propose a localised application of the Schwarz criterion, which is applicable with any multiscale candidate generating procedure fulfilling mild assumptions, and establish its theoretical consistency in estimating the number and locations of multiple change points under general assumptions permitting heavy tails and dependence. In particular, combined with a MOSUM-based candidate generating procedure, it attains minimax rate optimality in both detection lower bound and localisation for i.i.d. sub-Gaussian errors. Overall competitiveness of the proposed methodology compared to existing methods is shown through its theoretical and numerical performance.

Suggested Citation

  • Haeran Cho & Claudia Kirch, 2022. "Two-stage data segmentation permitting multiscale change points, heavy tails and dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 653-684, August.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:4:d:10.1007_s10463-021-00811-5
    DOI: 10.1007/s10463-021-00811-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-021-00811-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-021-00811-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, 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. Chun Yip Yau & Zifeng Zhao, 2016. "Inference for multiple change points in time series via likelihood ratio scan statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 895-916, September.
    4. 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.
    5. Michael Messer & Stefan Albert & Gaby Schneider, 2018. "The multiple filter test for change point detection in time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 589-607, August.
    6. 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.
    7. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
    8. Michalis K. Titsias & Christopher C. Holmes & Christopher Yau, 2016. "Statistical Inference in Hidden Markov Models Using k -Segment Constraints," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 200-215, March.
    9. Ngai Hang Chan & Chun Yip Yau & Rong-Mao Zhang, 2014. "Group LASSO for Structural Break Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 590-599, June.
    10. Tengyao Wang & Richard J. Samworth, 2018. "High dimensional change point estimation via sparse projection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 57-83, January.
    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. Lajos Horváth & Gregory Rice, 2014. "Rejoinder on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 287-290, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. S Kovács & P Bühlmann & H Li & A Munk, 2023. "Seeded binary segmentation: a general methodology for fast and optimal changepoint detection," Biometrika, Biometrika Trust, vol. 110(1), pages 249-256.
    2. Cho, Haeran & Fryzlewicz, Piotr, 2023. "Multiple change point detection under serial dependence: wild contrast maximisation and gappy Schwarz algorithm," LSE Research Online Documents on Economics 120085, London School of Economics and Political Science, LSE Library.
    3. McGonigle, Euan T. & Cho, Haeran, 2023. "Robust multiscale estimation of time-average variance for time series segmentation," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Bin & Zhang, Xinsheng & Liu, Yufeng, 2022. "High dimensional change point inference: Recent developments and extensions," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Yudong Chen & Tengyao Wang & Richard J. Samworth, 2022. "High‐dimensional, multiscale online changepoint detection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 234-266, February.
    3. Chen, Yudong & Wang, Tengyao & Samworth, Richard J., 2022. "High-dimensional, multiscale online changepoint detection," LSE Research Online Documents on Economics 113665, London School of Economics and Political Science, LSE Library.
    4. McGonigle, Euan T. & Cho, Haeran, 2023. "Robust multiscale estimation of time-average variance for time series segmentation," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    5. 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.
    6. 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.
    7. Jiang, Feiyu & Wang, Runmin & Shao, Xiaofeng, 2023. "Robust inference for change points in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    8. Claudia Kirch & Christina Stoehr, 2022. "Sequential change point tests based on U‐statistics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1184-1214, September.
    9. Cho, Haeran & Fryzlewicz, Piotr, 2023. "Multiple change point detection under serial dependence: wild contrast maximisation and gappy Schwarz algorithm," LSE Research Online Documents on Economics 120085, London School of Economics and Political Science, LSE Library.
    10. Cho, Haeran & Kirch, Claudia, 2022. "Bootstrap confidence intervals for multiple change points based on moving sum procedures," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    11. Horváth, Lajos & Rice, Gregory & Zhao, Yuqian, 2023. "Testing for changes in linear models using weighted residuals," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    12. Bertille Follain & Tengyao Wang & Richard J. Samworth, 2022. "High‐dimensional changepoint estimation with heterogeneous missingness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 1023-1055, July.
    13. Follain, Bertille & Wang, Tengyao & Samworth, Richard J., 2022. "High-dimensional changepoint estimation with heterogeneous missingness," LSE Research Online Documents on Economics 115014, London School of Economics and Political Science, LSE Library.
    14. Wu Wang & Xuming He & Zhongyi Zhu, 2020. "Statistical inference for multiple change‐point models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1149-1170, December.
    15. Davis, Richard A. & Hancock, Stacey A. & Yao, Yi-Ching, 2016. "On consistency of minimum description length model selection for piecewise autoregressions," Journal of Econometrics, Elsevier, vol. 194(2), pages 360-368.
    16. 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.
    17. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2020. "Change-point methods for multivariate time-series: paired vectorial observations," Statistical Papers, Springer, vol. 61(4), pages 1351-1383, August.
    18. Ardia, David & Dufays, Arnaud & Ordás Criado, Carlos, 2023. "Linking Frequentist and Bayesian Change-Point Methods," MPRA Paper 119486, University Library of Munich, Germany.
    19. 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.
    20. Cui, Junfeng & Wang, Guanghui & Zou, Changliang & Wang, Zhaojun, 2023. "Change-point testing for parallel data sets with FDR control," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:74:y:2022:i:4:d:10.1007_s10463-021-00811-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.