On the simplified pair-copula construction - Simply useful or too simplistic?

Authors:
Ingrid Hobæk Haff;Kjersti Aas;Arnoldo Frigessi
Affiliations:
Norwegian Computing Center, PB 114 Blindern, NO-0373 Oslo, Norway and Statistics for Innovation (sfi)2, Oslo, Norway;Norwegian Computing Center, PB 114 Blindern, NO-0373 Oslo, Norway and Statistics for Innovation (sfi)2, Oslo, Norway;Department of Biostatistics, University of Oslo, PB 1122 Blindern, NO-0317 Oslo, Norway and Statistics for Innovation (sfi)2, Oslo, Norway
Venue:
Journal of Multivariate Analysis
Year:
2010

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Abstract

Due to their high flexibility, yet simple structure, pair-copula constructions (PCCs) are becoming increasingly popular for constructing continuous multivariate distributions. However, inference requires the simplifying assumption that all the pair-copulae depend on the conditioning variables merely through the two conditional distribution functions that constitute their arguments, and not directly. In terms of standard measures of dependence, we express conditions under which a specific pair-copula decomposition of a multivariate distribution is of this simplified form. Moreover, we show that the simplified PCC in fact is a rather good approximation, even when the simplifying assumption is far from being fulfilled by the actual model.