IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v179y2023ics0167947322002286.html
   My bibliography  Save this article

Robust multiscale estimation of time-average variance for time series segmentation

Author

Listed:
  • McGonigle, Euan T.
  • Cho, Haeran

Abstract

There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often required in order to distinguish genuine changes from random fluctuations due to the noise. When serial dependence is present, using a single estimator of the noise level may not be appropriate. Instead, it is proposed to adopt a scale-dependent time-average variance constant that depends on the length of the data section in consideration, to gauge the level of the noise therein. Accordingly, an estimator that is robust to the presence of multiple mean shifts is developed. The consistency of the proposed estimator is shown under general assumptions permitting heavy-tailedness, and its use with two widely adopted data segmentation algorithms, the moving sum and the wild binary segmentation procedures, is discussed. The performance of the proposed estimator is illustrated through extensive simulation studies and on applications to the house price index and air quality data sets.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:csdana:v:179:y:2023:i:c:s0167947322002286
    DOI: 10.1016/j.csda.2022.107648
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947322002286
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2022.107648?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. Inder Tecuapetla-Gómez & Axel Munk, 2017. "Autocovariance Estimation in Regression with a Discontinuous Signal and m-Dependent Errors: A Difference-Based Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 346-368, 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. Marc Lavielle & Eric Moulines, 2000. "Least‐squares Estimation of an Unknown Number of Shifts in a Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 33-59, January.
    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. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    6. 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.
    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. 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.
    9. 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.
    10. 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.
    11. G. P. Nason & R. Von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
    12. 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.
    13. Marie Hušková & Claudia Kirch, 2010. "A note on studentized confidence intervals for the change-point," Computational Statistics, Springer, vol. 25(2), pages 269-289, June.
    Full references (including those not matched with items on IDEAS)

    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. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    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. 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.
    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. 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).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Shi, Xuesheng & Gallagher, Colin & Lund, Robert & Killick, Rebecca, 2022. "A comparison of single and multiple changepoint techniques for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    11. 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.
    12. 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.
    13. 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.
    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. 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.
    16. 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.
    17. Kang-Ping Lu & Shao-Tung Chang, 2023. "An Advanced Segmentation Approach to Piecewise Regression Models," Mathematics, MDPI, vol. 11(24), pages 1-23, December.
    18. Kim, Moosup & Lee, Taewook & Noh, Jungsik & Baek, Changryong, 2014. "Quasi-maximum likelihood estimation for multiple volatility shifts," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 50-60.
    19. Michael Messer & Gaby Schneider, 2017. "The shark fin function: asymptotic behavior of the filtered derivative for point processes in case of change points," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 253-272, July.
    20. 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.

    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:eee:csdana:v:179:y:2023:i:c:s0167947322002286. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.