A Goodness-of-fit Test for Copulas

We propose a new rank-based goodness-of-fit test for copulas. It uses the information matrix equality and so relates to the White (1982) specification test. The test avoids parametric specification of marginal distributions, it does not involve kernel weighting, bandwidth selection, or any other strategic choices, it is asymptotically pivotal with a standard distribution, and it is simple to compute compared to available alternatives. The finite-sample size of this type of tests is known to deviate from their nominal size based on asymptotic critical values, and bootstrapping critical values could be a preferred alternative. A power study shows that, in a bivariate setting, the test has reasonable properties compared to its competitors. We conclude with an application in which we apply the test to two stock indices.

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