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

By Jean-David Fermanian. 2012

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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.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fc863c45feb0c225665091623c42364c9efea223