IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v84y2022i3p933-972.html
   My bibliography  Save this article

On functional processes with multiple discontinuities

Author

Listed:
  • Jialiang Li
  • Yaguang Li
  • Tailen Hsing

Abstract

We consider the problem of estimating multiple change points for a functional data process. There are numerous examples in science and finance in which the process of interest may be subject to some sudden changes in the mean. The process data that are not in a close vicinity of any change point can be analysed by the usual nonparametric smoothing methods. However, the data close to change points and contain the most pertinent information of structural breaks need to be handled with special care. This paper considers a half‐kernel approach that addresses the inference of the total number, locations and jump sizes of the changes. Convergence rates and asymptotic distributional results for the proposed procedures are thoroughly investigated. Simulations are conducted to examine the performance of the approach, and a number of real data sets are analysed to provide an illustration.

Suggested Citation

  • Jialiang Li & Yaguang Li & Tailen Hsing, 2022. "On functional processes with multiple discontinuities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 933-972, July.
    • Handle: RePEc:bla:jorssb:v:84:y:2022:i:3:p:933-972
    DOI: 10.1111/rssb.12493
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssb.12493
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssb.12493?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
    ---><---

    References listed on IDEAS

    as
    1. Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410, June.
    2. Jeng‐Min Chiou & Pai‐Ling Li, 2007. "Functional clustering and identifying substructures of longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 679-699, September.
    3. István Berkes & Robertas Gabrys & Lajos Horváth & Piotr Kokoszka, 2009. "Detecting changes in the mean of functional observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 927-946, November.
    4. Oleksandr Gromenko & Piotr Kokoszka & Matthew Reimherr, 2017. "Detection of change in the spatiotemporal mean function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 29-50, January.
    5. Patrick Bardsley & Lajos Horváth & Piotr Kokoszka & Gabriel Young, 2017. "Change point tests in functional factor models with application to yield curves," Econometrics Journal, Royal Economic Society, vol. 20(1), pages 86-117, February.
    6. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    7. Chen, Ying & Niu, Linlin, 2014. "Adaptive dynamic Nelson–Siegel term structure model with applications," Journal of Econometrics, Elsevier, vol. 180(1), pages 98-115.
    8. Spokoiny, Vladimir G., 1998. "Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice," SFB 373 Discussion Papers 1998,1, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    10. Aston, John A.D. & Kirch, Claudia, 2012. "Detecting and estimating changes in dependent functional data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 204-220.
    11. Aue, Alexander & Gabrys, Robertas & Horváth, Lajos & Kokoszka, Piotr, 2009. "Estimation of a change-point in the mean function of functional data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2254-2269, November.
    12. Li, Jialiang & Zhang, Wenyang & Kong, Efang, 2018. "Factor models for asset returns based on transformed factors," Journal of Econometrics, Elsevier, vol. 207(2), pages 432-448.
    13. Jeng-Min Chiou & Hans-Georg Müller, 2014. "Linear manifold modelling of multivariate functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 605-626, June.
    14. Minya Xu & Ping-Shou Zhong & Wei Wang, 2016. "Detecting Variance Change-Points for Blocked Time Series and Dependent Panel Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 213-226, April.
    15. Grégoire, Gérard & Hamrouni, Zouhir, 2002. "Change Point Estimation by Local Linear Smoothing," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 56-83, October.
    16. 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.
    17. 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.
    18. Alexander Aue & Gregory Rice & Ozan Sönmez, 2018. "Detecting and dating structural breaks in functional data without dimension reduction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 509-529, June.
    19. Zhiming Xia & Peihua Qiu, 2015. "Jump information criterion for statistical inference in estimating discontinuous curves," Biometrika, Biometrika Trust, vol. 102(2), pages 397-408.
    20. Górecki, Tomasz & Horváth, Lajos & Kokoszka, Piotr, 2018. "Change point detection in heteroscedastic time series," Econometrics and Statistics, Elsevier, vol. 7(C), pages 63-88.
    21. Shuzhuan Zheng & Lijian Yang & Wolfgang K. Härdle, 2014. "A Smooth Simultaneous Confidence Corridor for the Mean of Sparse Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 661-673, 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. Trevor Harris & Bo Li & J. Derek Tucker, 2022. "Scalable multiple changepoint detection for functional data sequences," Environmetrics, John Wiley & Sons, Ltd., vol. 33(2), March.
    2. Horváth, Lajos & Rice, Gregory & Zhao, Yuqian, 2022. "Change point analysis of covariance functions: A weighted cumulative sum approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Han Lin Shang & Jiguo Cao & Peijun Sang, 2022. "Stopping time detection of wood panel compression: A functional time‐series approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1205-1224, November.
    4. J. Derek Tucker & Drew Yarger, 2024. "Elastic functional changepoint detection of climate impacts from localized sources," Environmetrics, John Wiley & Sons, Ltd., vol. 35(1), February.
    5. Stoehr, Christina & Aston, John A D & Kirch, Claudia, 2021. "Detecting changes in the covariance structure of functional time series with application to fMRI data," Econometrics and Statistics, Elsevier, vol. 18(C), pages 44-62.
    6. Rice, Gregory & Zhang, Chi, 2022. "Consistency of binary segmentation for multiple change-point estimation with functional data," Statistics & Probability Letters, Elsevier, vol. 180(C).
    7. Mengchen Wang & Trevor Harris & Bo Li, 2023. "Asynchronous Changepoint Estimation for Spatially Correlated Functional Time Series," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 157-176, March.
    8. Alessandro Casini & Pierre Perron, 2021. "Change-Point Analysis of Time Series with Evolutionary Spectra," Papers 2106.02031, arXiv.org, revised Jun 2021.
    9. Tadas Danielius & Alfredas Račkauskas, 2022. "Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process," Mathematics, MDPI, vol. 10(13), pages 1-27, June.
    10. B. Cooper Boniece & Lajos Horv'ath & Lorenzo Trapani, 2023. "On changepoint detection in functional data using empirical energy distance," Papers 2310.04853, arXiv.org.
    11. Dennis Schroers, 2024. "Robust Functional Data Analysis for Stochastic Evolution Equations in Infinite Dimensions," Papers 2401.16286, arXiv.org.
    12. Buddhananda Banerjee & Satyaki Mazumder, 2018. "A more powerful test identifying the change in mean of functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 691-715, June.
    13. Holger Dette & Kevin Kokot & Stanislav Volgushev, 2020. "Testing relevant hypotheses in functional time series via self‐normalization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 629-660, July.
    14. Chen, Likai & Wang, Weining & Wu, Wei Biao, 2019. "Inference of Break-Points in High-Dimensional Time Series," IRTG 1792 Discussion Papers 2019-013, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    15. Axel Bücher & Holger Dette & Florian Heinrichs, 2020. "Detecting deviations from second-order stationarity in locally stationary functional time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 1055-1094, August.
    16. Xu, Haotian & Wang, Daren & Zhao, Zifeng & Yu, Yi, 2022. "Change point inference in high-dimensional regression models under temporal dependence," LIDAM Discussion Papers ISBA 2022027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Zhou, Jie, 2011. "Maximum likelihood ratio test for the stability of sequence of Gaussian random processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2114-2127, June.
    18. Lajos Horváth & Piotr Kokoszka & Jeremy VanderDoes & Shixuan Wang, 2022. "Inference in functional factor models with applications to yield curves," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 872-894, November.
    19. Mengjia Yu & Xiaohui Chen, 2021. "Finite sample change point inference and identification for high‐dimensional mean vectors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 247-270, April.
    20. Li Cai & Lisha Li & Simin Huang & Liang Ma & Lijian Yang, 2020. "Oracally efficient estimation for dense functional data with holiday effects," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 282-306, March.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jorssb:v:84:y:2022:i:3:p:933-972. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.