IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v36y2021i3d10.1007_s00180-020-00994-0.html
   My bibliography  Save this article

On tests for symmetry and radial symmetry of bivariate copulas towards testing for ellipticity

Author

Listed:
  • Miriam Jaser

    (Technical University of Munich)

  • Aleksey Min

    (Technical University of Munich)

Abstract

Very simple non-parametric tests are proposed to detect symmetry and radial symmetry in the dependence structure of bivariate copula data. The performance of the proposed tests is illustrated in an intensive simulation study and compared to the one of similar more advanced tests, which do not require known margins. Further, a powerful non-parametric testing procedure to decide whether the dependence structure of the underlying bivariate copula data may be captured by an elliptical copula is provided. The testing procedure makes use of intrinsic properties of bivariate elliptical copulas such as symmetry, radial symmetry, and equality of Kendall’s tau and Blomqvist’s beta. The proposed tests as well as the testing procedure are very simple to use in applications. For an illustration of the testing procedure for ellipticity, financial and insurance data is analyzed.

Suggested Citation

  • Miriam Jaser & Aleksey Min, 2021. "On tests for symmetry and radial symmetry of bivariate copulas towards testing for ellipticity," Computational Statistics, Springer, vol. 36(3), pages 1-26, September.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-020-00994-0
    DOI: 10.1007/s00180-020-00994-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-020-00994-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-020-00994-0?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. Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2016. "Goodness-of-fit test for specification of semiparametric copula dependence models," Journal of Econometrics, Elsevier, vol. 193(1), pages 215-233.
    2. Matthias Fischer & Christian Kock & Stephan Schluter & Florian Weigert, 2009. "An empirical analysis of multivariate copula models," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 839-854.
    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. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    5. Christian Genest & Kilani Ghoudi & Louis-Paul Rivest, 1998. "“Understanding Relationships Using Copulas,” by Edward Frees and Emiliano Valdez, January 1998," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(3), pages 143-149.
    6. Bo Li & Marc G. Genton, 2013. "Nonparametric Identification of Copula Structures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 666-675, June.
    7. Christian Genest & Johanna Nešlehová, 2014. "On tests of radial symmetry for bivariate copulas," Statistical Papers, Springer, vol. 55(4), pages 1107-1119, November.
    8. Klugman, Stuart A. & Parsa, Rahul, 1999. "Fitting bivariate loss distributions with copulas," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 139-148, March.
    9. Friedrich Schmid & Rafael Schmidt, 2007. "Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(3), pages 323-354, November.
    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. Mangold, Benedikt, 2017. "New concepts of symmetry for copulas," FAU Discussion Papers in Economics 06/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics, revised 2017.
    2. Beare, Brendan K. & Seo, Juwon, 2020. "Randomization Tests Of Copula Symmetry," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1025-1063, December.
    3. Pavel Krupskii, 2017. "Copula-based measures of reflection and permutation asymmetry and statistical tests," Statistical Papers, Springer, vol. 58(4), pages 1165-1187, December.
    4. Quessy, Jean-François, 2021. "A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    5. 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.
    6. Gery Geenens & Arthur Charpentier & Davy Paindaveine, 2014. "Probit Transformation for Nonparametric Kernel Estimation of the Copula Density," Working Papers ECARES ECARES 2014-23, ULB -- Universite Libre de Bruxelles.
    7. Hua, Lei & Polansky, Alan & Pramanik, Paramahansa, 2019. "Assessing bivariate tail non-exchangeable dependence," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    8. Jean-François Quessy, 2021. "On nonparametric tests of multivariate meta-ellipticity," Statistical Papers, Springer, vol. 62(5), pages 2283-2310, October.
    9. Kojadinovic, Ivan, 2017. "Some copula inference procedures adapted to the presence of ties," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 24-41.
    10. Jaser Miriam & Haug Stephan & Min Aleksey, 2017. "A simple non-parametric goodness-of-fit test for elliptical copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 330-353, December.
    11. Genest, Christian & Masiello, Esterina & Tribouley, Karine, 2009. "Estimating copula densities through wavelets," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 170-181, April.
    12. Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
    13. Dominik Kortschak & Hansjörg Albrecher, 2009. "Asymptotic Results for the Sum of Dependent Non-identically Distributed Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 279-306, September.
    14. Chen, Xiaohong & Fan, Yanqin & Pouzo, Demian & Ying, Zhiliang, 2010. "Estimation and model selection of semiparametric multivariate survival functions under general censorship," Journal of Econometrics, Elsevier, vol. 157(1), pages 129-142, July.
    15. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodri­guez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2008. "On the construction of copulas and quasi-copulas with given diagonal sections," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 473-483, April.
    16. repec:hum:wpaper:sfb649dp2013-041 is not listed on IDEAS
    17. Ehab M. Almetwally & Aisha Fayomi & Maha E. Qura, 2024. "Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings," Mathematics, MDPI, vol. 12(12), pages 1-35, June.
    18. Hurlimann, Werner, 2004. "Fitting bivariate cumulative returns with copulas," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 355-372, March.
    19. Takaaki Koike & Marius Hofert, 2020. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations," Risks, MDPI, vol. 8(1), pages 1-33, January.
    20. Fang, Y. & Madsen, L., 2013. "Modified Gaussian pseudo-copula: Applications in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 292-301.

    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:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-020-00994-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.