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Test of independence and randomness based on the empirical copula process

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Abstract

Deheuvels (1981a) described a decomposition of the empirical copula process into a finite number of asymptotically mutually independent sub-processes whose joint limiting distribution is tractable under the hypothesis that a multivariate distribution is equal to the product of its margins. It is proved here that this result can be extended to the serial case and that the limiting processes have the same joint distribution as in the non-serial setting. As a consequences, linear rank statistics have the same asymptotic distribution in both contexts. It is also shown how these facts can be exploited to construct simple statistics for detecting dependence graphically and testing it formally. Simulation are used to explore the finite-sample behavior of these statistics, which are found to be powerful against varions types of alternatives.

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Authors and Affiliations

  1. Département de mathématiques et de statistique, Université Laval, G1K 7P4, Québec, Canada

    Christian Genest

  2. Service d'enseignement des méthodes quantitatives de gestion, HEC, G1K 7P4, Montréal, Canada

    Bruno Rémillard

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  1. Christian Genest
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  2. Bruno Rémillard
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Correspondence to Christian Genest.

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Genest, C., Rémillard, B. Test of independence and randomness based on the empirical copula process. Test 13, 335–369 (2004). https://doi.org/10.1007/BF02595777

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