IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v189y2022ics0047259x21001652.html
   My bibliography  Save this article

Extremal dependence measure for functional data

Author

Listed:
  • Kim, Mihyun
  • Kokoszka, Piotr

Abstract

Principal component analysis is one of the most fundamental tools of functional data analysis. It leads to an efficient representation of infinitely dimensional objects, like curves, by means of multivariate vectors of scores. We study the dependence between extremal values of the scores using the extremal dependence measure (EDM). The EDM has been proposed and studied for positive bivariate observations. After extending it to multivariate observations, we focus on its application to the vectors of scores of functional data. Estimated scores form a triangular array of dependent random variables. We derive condition guaranteeing that a suitable estimator of the EDM based on these scores converges to the population EDM and is asymptotically normal. These conditions are completely different from those encountered in the second-order theory of functional data. They are formulated within the framework of functional regular variation. Large sample theory is complemented by an application to intraday return curves for certain stocks and by a simulation study.

Suggested Citation

  • Kim, Mihyun & Kokoszka, Piotr, 2022. "Extremal dependence measure for functional data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x21001652
    DOI: 10.1016/j.jmva.2021.104887
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X21001652
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2021.104887?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. R de Fondeville & A C Davison, 2018. "High-dimensional peaks-over-threshold inference," Biometrika, Biometrika Trust, vol. 105(3), pages 575-592.
    2. Marc G. Genton & Simone A. Padoan & Huiyan Sang, 2015. "Multivariate max-stable spatial processes," Biometrika, Biometrika Trust, vol. 102(1), pages 215-230.
    3. Anthony W. Ledford & Jonathan A. Tawn, 2003. "Diagnostics for dependence within time series extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 521-543, May.
    4. Anthony W. Ledford & Jonathan A. Tawn, 1997. "Modelling Dependence within Joint Tail Regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 475-499.
    5. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
    6. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    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. Y Hoga, 2018. "A structural break test for extremal dependence in β-mixing random vectors," Biometrika, Biometrika Trust, vol. 105(3), pages 627-643.
    2. de Haan, Laurens & Neves, Cláudia & Peng, Liang, 2008. "Parametric tail copula estimation and model testing," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1260-1275, July.
    3. Cooley, Daniel & Davis, Richard A. & Naveau, Philippe, 2010. "The pairwise beta distribution: A flexible parametric multivariate model for extremes," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2103-2117, October.
    4. Ferreira, Helena & Ferreira, Marta, 2012. "Tail dependence between order statistics," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 176-192.
    5. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    6. Moreno Bevilacqua & Alfredo Alegria & Daira Velandia & Emilio Porcu, 2016. "Composite Likelihood Inference for Multivariate Gaussian Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 448-469, September.
    7. Ibrahim Ergen, 2014. "Tail dependence and diversification benefits in emerging market stocks: an extreme value theory approach," Applied Economics, Taylor & Francis Journals, vol. 46(19), pages 2215-2227, July.
    8. 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).
    9. Li, Feng & Kang, Yanfei, 2018. "Improving forecasting performance using covariate-dependent copula models," International Journal of Forecasting, Elsevier, vol. 34(3), pages 456-476.
    10. Jonathan B. Hill, 2004. "Strong Orthogonal Decompositions and Non-Linear Impulse Response Functions for Infinite Variance Processes," Econometrics 0401001, University Library of Munich, Germany, revised 16 Dec 2005.
    11. Kokoszka, Piotr & Kulik, Rafał, 2023. "Principal component analysis of infinite variance functional data," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    12. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).
    13. Cho, Min Ho & Kurtek, Sebastian & Bharath, Karthik, 2022. "Tangent functional canonical correlation analysis for densities and shapes, with applications to multimodal imaging data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    14. Zhang, Zhengjun & Zhu, Bin, 2016. "Copula structured M4 processes with application to high-frequency financial data," Journal of Econometrics, Elsevier, vol. 194(2), pages 231-241.
    15. Moore, Kyle & Zhou, Chen, 2014. "The determinants of systemic importance," LSE Research Online Documents on Economics 59289, London School of Economics and Political Science, LSE Library.
    16. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    17. Xiangying Meng & Xianhua Wei, 2018. "Systematic Correlation is Priced as Risk Factor," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 8(6), pages 1-2.
    18. Pushpa Dissanayake & Teresa Flock & Johanna Meier & Philipp Sibbertsen, 2021. "Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights," Mathematics, MDPI, vol. 9(21), pages 1-33, November.
    19. Fang Zhang & Zhengjun Zhang, 2020. "The tail dependence of the carbon markets: The implication of portfolio management," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-17, August.
    20. Michael Falk & René Michel, 2006. "Testing for Tail Independence in Extreme Value models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 261-290, June.

    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:189:y:2022:i:c:s0047259x21001652. 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.