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Detecting and dating structural breaks in functional data without dimension reduction

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  • Alexander Aue
  • Gregory Rice
  • Ozan Sönmez

Abstract

Methodology is proposed to uncover structural breaks in functional data that is ‘fully functional’ in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break detection procedure as well as for a break date estimator, assuming a fixed break size and a shrinking break size. The latter result is utilized to derive confidence intervals for the unknown break date. The main results highlight that the fully functional procedures perform best under conditions when analogous estimators based on functional principal component analysis are at their worst, namely when the feature of interest is orthogonal to the leading principal components of the data. The theoretical findings are confirmed by means of a Monte Carlo simulation study in finite samples. An application to annual temperature curves illustrates the practical relevance of the procedures proposed.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:80:y:2018:i:3:p:509-529
    DOI: 10.1111/rssb.12257
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    Cited by:

    1. 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.
    2. Lee, Sangyeol & Meintanis, Simos G. & Pretorius, Charl, 2022. "Monitoring procedures for strict stationarity based on the multivariate characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Alessandro Casini & Pierre Perron, 2021. "Change-Point Analysis of Time Series with Evolutionary Spectra," Papers 2106.02031, arXiv.org, revised Jun 2021.
    4. Franke, Jürgen & Hefter, Mario & Herzwurm, André & Ritter, Klaus & Schwaar, Stefanie, 2022. "Adaptive quantile computation for Brownian bridge in change-point analysis," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    5. 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).
    6. B. Cooper Boniece & Lajos Horv'ath & Lorenzo Trapani, 2023. "On changepoint detection in functional data using empirical energy distance," Papers 2310.04853, arXiv.org.
    7. 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.
    8. Qing Yang & Yu-Ning Li & Yi Zhang, 2020. "Change point detection for nonparametric regression under strongly mixing process," Statistical Papers, Springer, vol. 61(4), pages 1465-1506, August.
    9. 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.
    10. 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.
    11. Chen, Yichao & Pun, Chi Seng, 2019. "A bootstrap-based KPSS test for functional time series," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    12. 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.
    13. 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.
    14. Rice, Gregory & Zhang, Chi, 2022. "Consistency of binary segmentation for multiple change-point estimation with functional data," Statistics & Probability Letters, Elsevier, vol. 180(C).
    15. Holger Dette & Kevin Kokot, 2022. "Detecting relevant differences in the covariance operators of functional time series: a sup-norm approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 195-231, April.
    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. 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.

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