Bayesian copula selection

Authors:
David Huard;Guillaume ívin;Anne-Catherine Favre
Affiliations:
Institut National de la Recherche Scientifique, Centre Eau, Terre & Environnement, Quéé., Canada G1K 9A9;Institut National de la Recherche Scientifique, Centre Eau, Terre & Environnement, Quéé., Canada G1K 9A9;Institut National de la Recherche Scientifique, Centre Eau, Terre & Environnement, Quéé., Canada G1K 9A9
Venue:
Computational Statistics & Data Analysis
Year:
2006

Citing 3
Cited 13

Kendall's advanced theory of statistics

Kendall's advanced theory of statistics
Goodness-of-fit tests for copulas

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An Introduction to Copulas

An Introduction to Copulas

Copula model evaluation based on parametric bootstrap

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Copula, marginal distributions and model selection: a Bayesian note

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Testing the bivariate distribution of daily equity returns using copulas. An application to the Spanish stock market

Computational Statistics & Data Analysis
Three-stage semi-parametric estimation of T-copulas: Asymptotics, finite-sample properties and computational aspects

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Time-varying joint distribution through copulas

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Structural and Multidisciplinary Optimization
Reliability-based design optimization with confidence level under input model uncertainty due to limited test data

Structural and Multidisciplinary Optimization
Estimating discrete Markov models from various incomplete data schemes

Computational Statistics & Data Analysis
In mixed company: Bayesian inference for bivariate conditional copula models with discrete and continuous outcomes

Journal of Multivariate Analysis
Modelling multi-output stochastic frontiers using copulas

Computational Statistics & Data Analysis
Comparison study between probabilistic and possibilistic methods for problems under a lack of correlated input statistical information

Structural and Multidisciplinary Optimization
Unsupervised data classification using pairwise Markov chains with automatic copulas selection

Computational Statistics & Data Analysis
Penalized marginal likelihood estimation of finite mixtures of Archimedean copulas

Computational Statistics

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Abstract

In recent years, the use of copulas has grown extremely fast and with it, the need for a simple and reliable method to choose the right copula family. Existing methods pose numerous difficulties and none is entirely satisfactory. We propose a Bayesian method to select the most probable copula family among a given set. The copula parameters are treated as nuisance variables, and hence do not have to be estimated. Furthermore, by a parameterization of the copula density in terms of Kendall's @t, the prior on the parameter is replaced by a prior on @t, conceptually more meaningful. The prior on @t, common to all families in the set of tested copulas, serves as a basis for their comparison. Using simulated data sets, we study the reliability of the method and observe the following: (1) the frequency of successful identification approaches 100% as the sample size increases, (2) for weakly correlated variables, larger samples are necessary for reliable identification.