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Testing and estimating change-points in the covariance matrix of a high-dimensional time series

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  • Steland, Ansgar

Abstract

This paper studies methods for testing and estimating change-points in the covariance structure of a high-dimensional linear time series. The assumed framework allows for a large class of multivariate linear processes (including vector autoregressive moving average (VARMA) models) of growing dimension and spiked covariance models. The approach uses bilinear forms of the centered or non-centered sample variance–covariance matrix. Change-point testing and estimation are based on maximally selected weighted cumulated sum (CUSUM) statistics. Large sample approximations under a change-point regime are provided including a multivariate CUSUM transform of increasing dimension. For the unknown asymptotic variance and covariance parameters associated to (pairs of) CUSUM statistics we propose consistent estimators. Based on weak laws of large numbers for their sequential versions, we also consider stopped sample estimation where observations until the estimated change-point are used. Finite sample properties of the procedures are investigated by simulations and their application is illustrated by analyzing a real data set from environmetrics.

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  • Steland, Ansgar, 2020. "Testing and estimating change-points in the covariance matrix of a high-dimensional time series," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:jmvana:v:177:y:2020:i:c:s0047259x18305104
    DOI: 10.1016/j.jmva.2019.104582
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    Cited by:

    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. Stergios B. Fotopoulos & Abhishek Kaul & Vasileios Pavlopoulos & Venkata K. Jandhyala, 2024. "Adaptive parametric change point inference under covariance structure changes," Statistical Papers, Springer, vol. 65(5), pages 2887-2913, July.
    3. Steland, Ansgar, 2024. "Flexible nonlinear inference and change-point testing of high-dimensional spectral density matrices," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    4. Anibal Emiliano Da Silva Neto & Jesús Gonzalo & Jean‐Yves Pitarakis, 2021. "Uncovering Regimes in Out of Sample Forecast Errors from Predictive Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(3), pages 713-741, June.
    5. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    6. Monika Bours & Ansgar Steland, 2021. "Large‐sample approximations and change testing for high‐dimensional covariance matrices of multivariate linear time series and factor models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 610-654, June.
    7. Liu, Bin & Zhang, Xinsheng & Liu, Yufeng, 2022. "High dimensional change point inference: Recent developments and extensions," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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