Pair-copula constructions of multiple dependence |
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Authors: | Kjersti Aas Claudia Czado Henrik Bakken |
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Affiliation: | a The Norwegian Computing Centre, P.O. Box 114, Blindern, N-0314 Oslo, Norway b Technische Universität, München, Germany c Centre for Statistics for Innovation, University of Oslo and the Norwegian Computing Centre, Oslo, Norway d The Norwegian University of Science and Technology, Trondheim, Norway |
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Abstract: | Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of pair-copulae, acting on two variables at a time. We use the pair-copula decomposition of a general multivariate distribution and propose a method for performing inference. The model construction is hierarchical in nature, the various levels corresponding to the incorporation of more variables in the conditioning sets, using pair-copulae as simple building blocks. Pair-copula decomposed models also represent a very flexible way to construct higher-dimensional copulae. We apply the methodology to a financial data set. Our approach represents the first step towards the development of an unsupervised algorithm that explores the space of possible pair-copula models, that also can be applied to huge data sets automatically. |
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Keywords: | Pair-copulae Vines Conditional distribution Decomposition Multivariate distribution |
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