"Genest, Christian, Bruno Rémillard, David Beaudoin, "Goodness-of-fit tests for Copulas: A review and a power study", Insurance: Mathematics and Economics, Vol. 44, No. 2, (April 2009), pp. 199-213.

Abstract: Many proposals have been made recently for goodness-of-fit testing of copula models. After reviewing them briefly, the authors concentrate on “blanket tests”, i.e., those whose implementation requires neither an arbitrary categorization of the data nor any strategic choice of smoothing parameter, weight function, kernel, window, etc. The authors present a critical review of these procedures and suggest new ones. They describe and interpret the results of a large Monte Carlo experiment designed to assess the effect of the sample size and the strength of dependence on the level and power of the blanket tests for various combinations of copula models under the null hypothesis and the alternative. To circumvent problems in the determination of the limiting distribution of the test statistics under composite null hypotheses, they recommend the use of a double parametric bootstrap procedure, whose implementation is detailed. They conclude with a number of practical recommendations.

Keywords: Anderson-Darling statistic, Copula, Cramér–von Mises statistic, Gaussian process, Goodness-of-fit, Kendall’s tau, Kolmogorov–Smirnov statistic, Monte Carlo simulation, Parametric bootstrap, Powerstudy, Pseudo-observations, P-values.

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