IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v177y2020ics0047259x18305104.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X18305104
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2019.104582?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. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Johnstone, Iain M. & Lu, Arthur Yu, 2009. "On Consistency and Sparsity for Principal Components Analysis in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 682-693.
    3. Sancetta, Alessio, 2008. "Sample covariance shrinkage for high dimensional dependent data," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 949-967, May.
    4. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
    5. Steland, Ansgar & von Sachs, Rainer, 2018. "Asymptotics for high-dimensional covariance matrices and quadratic forms with applications to the trace functional and shrinkage," LIDAM Reprints ISBA 2018020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Shen, Dan & Shen, Haipeng & Marron, J.S., 2013. "Consistency of sparse PCA in High Dimension, Low Sample Size contexts," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 317-333.
    7. Haeran Cho & Piotr Fryzlewicz, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 475-507, March.
    8. Horváth, Lajos & Rice, Gregory, 2019. "Asymptotics for empirical eigenvalue processes in high-dimensional linear factor models," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 138-165.
    9. Han, Xu & Inoue, Atsushi, 2015. "Tests For Parameter Instability In Dynamic Factor Models," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1117-1152, October.
    10. Cho, Haeran & Fryzlewicz, Piotr, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," LSE Research Online Documents on Economics 57147, London School of Economics and Political Science, LSE Library.
    11. Marsaglia, George & Tsang, Wai Wan & Wang, Jingbo, 2003. "Evaluating Kolmogorov's Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i18).
    12. 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.
    13. Y. Yu & T. Wang & R. J. Samworth, 2015. "A useful variant of the Davis–Kahan theorem for statisticians," Biometrika, Biometrika Trust, vol. 102(2), pages 315-323.
    14. Kouritzin, Michael A., 1995. "Strong approximation for cross-covariances of linear variables with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 343-353, December.
    15. Steland, Ansgar & von Sachs, Rainer, 2018. "Asymptotics for high-dimensional covariance matrices and quadratic forms with applications to the trace functional and shrinkage," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2816-2855.
    16. Ferger, Dietmar, 2018. "On the supremum of a Brownian bridge standardized by its maximizing point with applications to statistics," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 63-69.
    17. Steland, Ansgar & von Sachs, Rainer, 2017. "Large-Sample Approximations for Variance-Covariance Matrices of High-Dimensional Time Series," LIDAM Reprints ISBA 2017015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    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. 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).

    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. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    2. Li, Degui, 2024. "Estimation of Large Dynamic Covariance Matrices: A Selective Review," Econometrics and Statistics, Elsevier, vol. 29(C), pages 16-30.
    3. Barigozzi, Matteo & Cho, Haeran & Fryzlewicz, Piotr, 2018. "Simultaneous multiple change-point and factor analysis for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 206(1), pages 187-225.
    4. Ma, Chenchen & Tu, Yundong, 2023. "Group fused Lasso for large factor models with multiple structural breaks," Journal of Econometrics, Elsevier, vol. 233(1), pages 132-154.
    5. 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.
    6. Steland, Ansgar & von Sachs, Rainer, 2018. "Asymptotics for high-dimensional covariance matrices and quadratic forms with applications to the trace functional and shrinkage," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2816-2855.
    7. 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".
    8. Cho, Haeran & Korkas, Karolos K., 2022. "High-dimensional GARCH process segmentation with an application to Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 23(C), pages 187-203.
    9. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    10. Ansgar Steland, 2018. "Shrinkage for covariance estimation: asymptotics, confidence intervals, bounds and applications in sensor monitoring and finance," Statistical Papers, Springer, vol. 59(4), pages 1441-1462, December.
    11. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    12. Bin Liu & Cheng Zhou & Xinsheng Zhang & Yufeng Liu, 2020. "A unified data‐adaptive framework for high dimensional change point detection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 933-963, September.
    13. Pang, Tianxiao & Du, Lingjie & Chong, Terence Tai-Leung, 2021. "Estimating multiple breaks in nonstationary autoregressive models," Journal of Econometrics, Elsevier, vol. 221(1), pages 277-311.
    14. Aaron Paul Lowther & Rebecca Killick & Idris Arthur Eckley, 2023. "Detecting changes in mixed‐sampling rate data sequences," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    15. 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.
    16. Hajra Siddiqa & Sajid Ali & Ismail Shah, 2021. "Most recent changepoint detection in censored panel data," Computational Statistics, Springer, vol. 36(1), pages 515-540, March.
    17. Steland, Ansgar & von Sachs, Rainer, 2016. "Asymptotics for High–Dimensional Covariance Matrices and Quadratic Forms with Applications to the Trace Functional and Shrinkage," LIDAM Discussion Papers ISBA 2016038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Ping‐Shou Zhong & Jun Li & Piotr Kokoszka, 2021. "Multivariate analysis of variance and change points estimation for high‐dimensional longitudinal data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 375-405, June.
    19. Chen, Cathy Yi-hsuan & Okhrin, Yarema & Wang, Tengyao, 2022. "Monitoring network changes in social media," LSE Research Online Documents on Economics 113742, London School of Economics and Political Science, LSE Library.
    20. 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.

    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:jmvana:v:177:y:2020:i:c:s0047259x18305104. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.