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Copulae in Mathematical and Quantitative Finance pp 91–114Cite as

Assessing and Modeling Asymmetry in Bivariate Continuous Data

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Part of the book series: Lecture Notes in Statistics ((LNSP,volume 213))

Abstract

A bivariate copula is the cumulative distribution function of a pair (U, V ) of uniform random variables. This copula is said to be symmetric if and only if (V, U) and (U, V ) have the same distribution. Many standard bivariate parametric families of copulas have this property; Archimedean and meta-elliptical copulas are prime examples. In practice, however, dependence is often asymmetric. This paper revisits key aspects of this issue from a modeling perspective. Measures of asymmetry and rank-based estimators thereof are discussed, along with recently proposed tests of symmetry. Several techniques for the construction of asymmetric dependence structures are critically reviewed. A hydrological data set is used for illustration purposes.

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Acknowledgments

Thanks are due to Tomáš Bacigál for providing the hydrological data set and his R code. The assistance of Marius Hofert and Ivan Kojadinovic with the R implementation of some of the simulation and estimation procedures used here is also gratefully acknowledged. Funding in partial support of this work was provided by the Canada Research Chairs Program, the Natural Sciences and Engineering Research Council of Canada, and the Fonds de recherche du Québec—Nature et technologies.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada

    Christian Genest & Johanna G. Nešlehová

Authors
  1. Christian Genest
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  2. Johanna G. Nešlehová
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Correspondence to Christian Genest .

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Editors and Affiliations

  1. Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, ul. Banacha 2, Warszawa, 02097, Poland

    Piotr Jaworski

  2. School of Economics and Management, Free University of Bozen-Bolzano, Piazza Università 1, Bozen, 39100, Italy

    Fabrizio Durante

  3. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

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Genest, C., Nešlehová, J.G. (2013). Assessing and Modeling Asymmetry in Bivariate Continuous Data. In: Jaworski, P., Durante, F., Härdle, W. (eds) Copulae in Mathematical and Quantitative Finance. Lecture Notes in Statistics(), vol 213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35407-6_5

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