IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v191y2022ics0047259x22000471.html

t-copula from the viewpoint of tail dependence matrices

Author

Listed:
  • Shyamalkumar, Nariankadu D.
  • Tao, Siyang

Abstract

The tail dependence coefficient is a bivariate measure of dependence in the tail, and the Tail Dependence Matrix (TDM) is a bidimensional array of these coefficients corresponding to a random vector. The TDM serves as a parsimonious measure of multivariate tail dependence akin to the correlation matrix in the context of dependence. The set of all TDMs corresponding to d-dimensional random vectors is a convex polytope with an intricate description known only for d up to six, with both its numbers of facets and vertices growing at least exponentially in d. We posit that the richness of its subset that a copula family can accommodate is a practically vital feature to be considered in its choice for modeling in the presence of tail dependence. In this paper, our focus is on the t-copula family, which is a popular choice for parametric modeling in risk management and financial econometrics. We discuss some geometric properties of the subset of TDMs supported by the t-copula family and provide an efficient algorithm to determine the t-copula that best captures the tail dependence specified by a target TDM.

Suggested Citation

  • Shyamalkumar, Nariankadu D. & Tao, Siyang, 2022. "t-copula from the viewpoint of tail dependence matrices," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:jmvana:v:191:y:2022:i:c:s0047259x22000471
    DOI: 10.1016/j.jmva.2022.105027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X22000471
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2022.105027?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Rafael Schmidt & Ulrich Stadtmüller, 2006. "Non‐parametric Estimation of Tail Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 307-335, June.
    2. Karolyi, G Andrew & Stulz, Rene M, 1996. "Why Do Markets Move Together? An Investigation of U.S.-Japan Stock Return Comovements," Journal of Finance, American Finance Association, vol. 51(3), pages 951-986, July.
    3. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    4. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496, December.
    5. W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 1-14.
    6. Krause, Daniel & Scherer, Matthias & Schwinn, Jonas & Werner, Ralf, 2018. "Membership testing for Bernoulli and tail-dependence matrices," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 240-260.
    7. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    8. Kofman, Paul & Koedijk, Kees & Campbell, Rachel, 2002. "Increased Correlation in Bear markets: A Downside Risk Perspective," CEPR Discussion Papers 3172, Centre for Economic Policy Research.
    9. Krupskii, Pavel & Joe, Harry, 2019. "Nonparametric estimation of multivariate tail probabilities and tail dependence coefficients," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 147-161.
    10. Donnelly, Catherine & Embrechts, Paul, 2010. "The Devil is in the Tails: Actuarial Mathematics and the Subprime Mortgage Crisis," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 1-33, May.
    11. Beine, Michel & Cosma, Antonio & Vermeulen, Robert, 2010. "The dark side of global integration: Increasing tail dependence," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 184-192, January.
    12. J. Rosco & Harry Joe, 2013. "Measures of tail asymmetry for bivariate copulas," Statistical Papers, Springer, vol. 54(3), pages 709-726, August.
    13. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
    14. Frahm, Gabriel & Junker, Markus & Schmidt, Rafael, 2005. "Estimating the tail-dependence coefficient: Properties and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 80-100, August.
    15. 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.
    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. Daniela I. Flores-Silva & Miguel A. Sordo & Alfonso Su'arez-Llorens, 2025. "Probability equivalent level for CoVaR and VaR in bivariate Student-\textit{t} copulas with application to foreign exchange risk monitoring," Papers 2510.15934, arXiv.org.

    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. Nikoloulopoulos, Aristidis K. & Joe, Harry & Li, Haijun, 2012. "Vine copulas with asymmetric tail dependence and applications to financial return data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3659-3673.
    2. Aleksy Leeuwenkamp & Wentao Hu, 2023. "New general dependence measures: construction, estimation and application to high-frequency stock returns," Papers 2309.00025, arXiv.org.
    3. Conlon, Thomas & Cotter, John & Ropotos, Ioannis, 2026. "Drivers of firm-level tail dependence: A machine learning approach," Journal of Economic Dynamics and Control, Elsevier, vol. 182(C).
    4. Albuquerque, Rui & Vega, Clara, 2006. "Asymmetric Information in the Stock Market: Economic News and Co-movement," CEPR Discussion Papers 5598, Centre for Economic Policy Research.
    5. Reboredo, Juan C., 2012. "Do food and oil prices co-move?," Energy Policy, Elsevier, vol. 49(C), pages 456-467.
    6. Nicolas, Maxime L.D., 2026. "Tail risk exposure and the cross section of expected stock returns," Journal of Banking & Finance, Elsevier, vol. 184(C).
    7. Reboredo, Juan C., 2011. "How do crude oil prices co-move?: A copula approach," Energy Economics, Elsevier, vol. 33(5), pages 948-955, September.
    8. Aguilar, Mike & Hill, Jonathan B., 2015. "Robust score and portmanteau tests of volatility spillover," Journal of Econometrics, Elsevier, vol. 184(1), pages 37-61.
    9. Trabelsi, Nader, 2017. "Asymmetric tail dependence between oil price shocks and sectors of Saudi Arabia System," The Journal of Economic Asymmetries, Elsevier, vol. 16(C), pages 26-41.
    10. Shogo Kato & Toshinao Yoshiba & Shinto Eguchi, 2022. "Copula-based measures of asymmetry between the lower and upper tail probabilities," Statistical Papers, Springer, vol. 63(6), pages 1907-1929, December.
    11. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate conditional versions of Spearman's rho and related measures of tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1123-1140, July.
    12. Carsten Bormann & Melanie Schienle, 2020. "Detecting Structural Differences in Tail Dependence of Financial Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 380-392, April.
    13. 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.
    14. Chollete, Lorán & de la Peña, Victor & Lu, Ching-Chih, 2011. "International diversification: A copula approach," Journal of Banking & Finance, Elsevier, vol. 35(2), pages 403-417, February.
    15. Herrera, R. & Eichler, S., 2011. "Extreme dependence with asymmetric thresholds: Evidence for the European Monetary Union," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2916-2930, November.
    16. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2017. "The kidnapping of Europe: High-order moments' transmission between developed and emerging markets," Emerging Markets Review, Elsevier, vol. 31(C), pages 96-115.
    17. Dorota Witkowska & Krzysztof Kompa & Aleksandra Matuszewska-Janica, 2012. "Analysis of Linkages between Central and Eastern European Capital Markets," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 12, pages 19-34.
    18. Roman Matkovskyy, 2019. "Extremal Economic (Inter)Dependence Studies: A Case of the Eastern European Countries," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(3), pages 667-698, September.
    19. Paulusch, Joachim & Schlütter, Sebastian, 2022. "Sensitivity-implied tail-correlation matrices," Journal of Banking & Finance, Elsevier, vol. 134(C).
    20. Chollete, Lorán & de la Peña, Victor & Lu, Ching-Chih, 2012. "International diversification: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 36(3), pages 871-885.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:191:y:2022:i:c:s0047259x22000471. 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.