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An Overview of the Goodness-of-Fit Test Problem for Copulas

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Copulae in Mathematical and Quantitative Finance

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

Abstract

We review the main “omnibus procedures” for goodness-of-fit (GOF) testing for copulas: tests based on the empirical copula process, on probability integral transformations (PITs), on Kendall’s dependence function, etc., and some corresponding reductions of dimension techniques. The problems of finding asymptotic distribution-free test statistics and the calculation of reliable p-values are discussed. Some particular cases, like convenient tests for time-dependent copulas, for Archimedean or extreme-value copulas, etc., are dealt with. Finally, the practical performances of the proposed approaches are briefly summarized.

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  1. Department of Finance, Ensae-Crest, Malakoff, France

    Jean-David Fermanian

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  1. Jean-David Fermanian
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Correspondence to Jean-David Fermanian .

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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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Fermanian, JD. (2013). An Overview of the Goodness-of-Fit Test Problem for Copulas. 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_4

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