Simplified pair copula constructions: Limitations and extensions

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Simplified pair copula constructions: Limitations and extensions

TitleSimplified pair copula constructions: Limitations and extensions
Publication TypeJournal Article
Year of Publication2013
AuthorsStoeber, J, Joe, H, Czado, C
JournalJournal of Multivariate Analysis
Date PublishedAUG
Type of ArticleArticle
KeywordsArchimedean copula, Conditional distribution, Elliptical copula, Pair copula construction
AbstractSo-called pair copula constructions (PCCs), specifying multivariate distributions only in terms of bivariate building blocks (pair copulas), constitute a flexible class of dependence models. To keep them tractable for inference and model selection, the simplifying assumption, that copulas of conditional distributions do not depend on the values of the variables which they are conditioned on, is popular. We show that the only Archimedean copulas in dimension d >= 3 which are of the simplified type are those based on the Gamma Laplace transform or its extension, while the Student-t copulas are the only one arising from a scale mixture of Normals. Further, we illustrate how PCCs can be adapted for situations where conditional copulas depend on values which are conditioned on, and demonstrate a technique to assess the distance of a multivariate distribution from a nearby distribution that satisfies the simplifying assumption. (C) 2013 Published by Elsevier Inc.