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Measures of tail asymmetry for bivariate copulas

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  • J. Rosco
  • Harry Joe

Abstract

Three tail asymmetry measures for bivariate copulas are introduced using two different approaches—univariate skewness of a projection and distance between a copula and its survival/reflected copula. We compare the asymmetry measures based on certain desirable properties. Bounds for each measure are obtained and also copulas which attain these extreme values are identified. Two data examples show the amount of asymmetry that might be expected in practice. Copyright Springer-Verlag 2013

Suggested Citation

  • J. Rosco & Harry Joe, 2013. "Measures of tail asymmetry for bivariate copulas," Statistical Papers, Springer, vol. 54(3), pages 709-726, August.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:709-726
    DOI: 10.1007/s00362-012-0457-y
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    References listed on IDEAS

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    Cited by:

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    3. 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.
    4. Nadarajah, Saralees, 2015. "Expansions for bivariate copulas," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 77-84.
    5. Werner Hürlimann, 2017. "A comprehensive extension of the FGM copula," Statistical Papers, Springer, vol. 58(2), pages 373-392, June.
    6. Christian Genest & Johanna Nešlehová, 2014. "On tests of radial symmetry for bivariate copulas," Statistical Papers, Springer, vol. 55(4), pages 1107-1119, November.
    7. Yuichi Goto & Tobias Kley & Ria Van Hecke & Stanislav Volgushev & Holger Dette & Marc Hallin, 2021. "The Integrated Copula Spectrum," Working Papers ECARES 2021-29, ULB -- Universite Libre de Bruxelles.
    8. 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.
    9. Billio Monica & Frattarolo Lorenzo & Guégan Dominique, 2021. "Multivariate radial symmetry of copula functions: finite sample comparison in the i.i.d case," Dependence Modeling, De Gruyter, vol. 9(1), pages 43-61, January.
    10. Pavel Krupskii, 2017. "Copula-based measures of reflection and permutation asymmetry and statistical tests," Statistical Papers, Springer, vol. 58(4), pages 1165-1187, December.
    11. Tarik Bahraoui & Nikolai Kolev, 2021. "New Measure of the Bivariate Asymmetry," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 421-448, February.
    12. Shyamalkumar, Nariankadu D. & Tao, Siyang, 2022. "t-copula from the viewpoint of tail dependence matrices," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    13. Marius Hofert & Johanna F. Ziegel, 2021. "Matrix-Tilted Archimedean Copulas," Risks, MDPI, vol. 9(4), pages 1-24, April.

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