IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v119y2013icp61-70.html
   My bibliography  Save this article

Empirical and sequential empirical copula processes under serial dependence

Author

Listed:
  • Bücher, Axel
  • Volgushev, Stanislav

Abstract

Empirical and sequential empirical copula processes play a central role for statistical inference on copulas. However, as pointed out by Johan Segers [J. Segers, Asymptotics of empirical copula processes under non-restrictive smoothness assumptions, Bernoulli 18 (3) (2012) 764–782] the usual assumptions under which these processes have been studied so far are too restrictive. In this paper, we provide a unified approach to the analysis of empirical and sequential empirical copula processes that circumvents those restrictive assumptions in a very general setting. In particular, our methods allow for an easy analysis of copula processes and appropriate bootstrap approximations in the setting of sequentially dependent data. One particularly useful finding is that certain sequential empirical copula processes converge without any smoothness assumptions on the copula.

Suggested Citation

  • Bücher, Axel & Volgushev, Stanislav, 2013. "Empirical and sequential empirical copula processes under serial dependence," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 61-70.
    • Handle: RePEc:eee:jmvana:v:119:y:2013:i:c:p:61-70
    DOI: 10.1016/j.jmva.2013.04.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13000493
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.04.003?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. Dehling, Herold & Durieu, Olivier, 2011. "Empirical processes of multidimensional systems with multiple mixing properties," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1076-1096, May.
    2. Mokkadem, Abdelkader, 1988. "Mixing properties of ARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 309-315, September.
    3. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
    4. Bücher, Axel & Dette, Holger, 2010. "A note on bootstrap approximations for the empirical copula process," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1925-1932, December.
    5. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    6. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate extensions of Spearman's rho and related statistics," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 407-416, February.
    8. Paul Doukhan & Jean-David Fermanian & Gabriel Lang, 2009. "An empirical central limit theorem with applications to copulas under weak dependence," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 65-87, February.
    9. Rémillard, Bruno & Papageorgiou, Nicolas & Soustra, Frédéric, 2012. "Copula-based semiparametric models for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 30-42.
    10. D. Marinucci, 2005. "The Empirical Process for Bivariate Sequences with Long Memory," Statistical Inference for Stochastic Processes, Springer, vol. 8(2), pages 205-223, September.
    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. Seo, Juwon, 2018. "Tests of stochastic monotonicity with improved power," Journal of Econometrics, Elsevier, vol. 207(1), pages 53-70.
    2. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
    3. Beare, Brendan K. & Seo, Juwon, 2020. "Randomization Tests Of Copula Symmetry," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1025-1063, December.
    4. Kiriliouk, Anna & Segers, Johan & Tsukahara, Hideatsu, 2019. "On Some Resampling Procedures with the Empirical Beta Copula," LIDAM Discussion Papers ISBA 2019012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Christian Genest & Johanna Nešlehová, 2014. "On tests of radial symmetry for bivariate copulas," Statistical Papers, Springer, vol. 55(4), pages 1107-1119, November.
    6. Bucher, Axel & Kojadinovic, Ivan, 2013. "A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing," LIDAM Discussion Papers ISBA 2013029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105, arXiv.org.
    8. Bücher, Axel & Ruppert, Martin, 2013. "Consistent testing for a constant copula under strong mixing based on the tapered block multiplier technique," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 208-229.
    9. Bucher, Axel & Segers, Johan & Volgushev, Stanislav, 2013. "When uniform weak convergence fails: empirical processes for dependence functions via epi- and hypographs," LIDAM Discussion Papers ISBA 2013019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    11. Fuchs, Sebastian & Tschimpke, Marco, 2024. "A novel positive dependence property and its impact on a popular class of concordance measures," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    12. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
    13. Salim Bouzebda, 2023. "On Weak Convergence of the Bootstrap Copula Empirical Process with Random Resample Size," Stats, MDPI, vol. 6(1), pages 1-16, February.
    14. Bianchi, Pascal & Elgui, Kevin & Portier, François, 2023. "Conditional independence testing via weighted partial copulas," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    15. Kojadinovic, Ivan & Rohmer, Tom & Segers, Johan, 2013. "Detecting changes in cross-sectional dependence in multivariate time series," LIDAM Discussion Papers ISBA 2013051, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Bücher, Axel & Kojadinovic, Ivan & Rohmer, Tom & Segers, Johan, 2014. "Detecting changes in cross-sectional dependence in multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 111-128.
    17. Hobæk Haff, Ingrid & Segers, Johan, 2015. "Nonparametric estimation of pair-copula constructions with the empirical pair-copula," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 1-13.
    18. Jean-David Fermanian & Dragan Radulovic & Marten Wegkamp, 2013. "A Asymptotic Total Variation Test for Copulas," Working Papers 2013-25, Center for Research in Economics and Statistics.
    19. Kojadinovic, Ivan & Stemikovskaya, Kristina, 2019. "Subsampling (weighted smooth) empirical copula processes," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 704-723.
    20. Bücher Axel & Jaser Miriam & Min Aleksey, 2021. "Detecting departures from meta-ellipticity for multivariate stationary time series," Dependence Modeling, De Gruyter, vol. 9(1), pages 121-140, January.

    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:119:y:2013:i:c:p:61-70. 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.