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Goodness-of-fit Procedures for Copula Models Based on the Probability Integral Transformation

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Author Info
CHRISTIAN GENEST
JEAN-FRANÇOIS QUESSY
BRUNO RÉMILLARD
Abstract

Wang & Wells ["J. Amer. Statist. Assoc." 95 (2000) 62] describe a non-parametric approach for checking whether the dependence structure of a random sample of censored bivariate data is appropriately modelled by a given family of Archimedean copulas. Their procedure is based on a truncated version of the Kendall process introduced by Genest & Rivest ["J. Amer. Statist. Assoc." 88 (1993) 1034] and later studied by Barbe "et al". ["J. Multivariate Anal." 58 (1996) 197]. Although Wang & Wells (2000) determine the asymptotic behaviour of their truncated process, their model selection method is based exclusively on the observed value of its "L"-super-2-norm. This paper shows how to compute asymptotic "p"-values for various goodness-of-fit test statistics based on a non-truncated version of Kendall's process. Conditions for weak convergence are met in the most common copula models, whether Archimedean or not. The empirical behaviour of the proposed goodness-of-fit tests is studied by simulation, and power comparisons are made with a test proposed by Shih ["Biometrika" 85 (1998) 189] for the gamma frailty family. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..

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Article provided by Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association in its journal Scandinavian Journal of Statistics.

Volume (Year): 33 (2006)
Issue (Month): 2 ()
Pages: 337-366
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Handle: RePEc:bla:scjsta:v:33:y:2006:i:2:p:337-366

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  2. Oriol Roch Casellas & Antonio Alegre Escolano, 2005. "Testing the bivariate distribution of daily equity returns using copulas. An application to the Spanish stock market," Working Papers in Economics 143, Universitat de Barcelona. Espai de Recerca en Economia. [Downloadable!]
  3. Antai Wang, 2007. "The Analysis of Bivariate Truncated Data Using the Clayton Copula Model," International Journal of Biostatistics, Berkeley Electronic Press, vol. 3(1), pages 1050-1050. [Downloadable!] (restricted)
  4. Charpentier, Arthur & Segers, Johan, 2006. "Convergence of Archimedean copulas," Discussion Paper 28, Tilburg University, Center for Economic Research. [Downloadable!]
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