A Asymptotic Total Variation Test for Copulas
We propose a new goodness-of-fit test for copulas, based on empirical copula processes and nonparametric bootstrap counterparts. The standard Kolmogorov-Smirnov type test for copulas that takes the supremum of the empirical copula process indexed by orthants is extended by test statistics based on the supremum of the empirical copula process indexed by families of Ln disjoint boxes, with Ln slowly tending to infinity. Although the underlying empirical process does not converge, the critical values of our new test statistic can be consistently estimated by nonparametric bootstrap techniques, under simple or composite null assumptions. Simulations confirm that the power of the new procedure is oftentimes higher than the power of the standard Kolmogorov-Smirnov or the Cramer-von Mises tests for copulas
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- Bücher, Axel & Dette, Holger, 2010. "A note on bootstrap approximations for the empirical copula process," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1925-1932, December.
- Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
- Bruno Rémillard & Olivier Scaillet, 2006.
"Testing For Equality Between Two Copulas,"
Swiss Finance Institute Research Paper Series
07-24, Swiss Finance Institute.
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