## Bayesian model selection for D-vine pair-copula constructions.(English. French summary)Zbl 1219.62048

Summary: In recent years analyses of dependence structures using copulas have become more popular than the standard correlation analysis. Starting from K. Aas et al. [Insur. Math. Econ. 44, No. 2, 182–198 (2009; Zbl 1165.60009)] regular vine pair-copula constructions (PCCs) are considered the most flexible class of multivariate copulas. PCCs are involved objects but (conditional) independence present in data can simplify and reduce them significantly. The authors detect (conditional) independence in a particular vine PCC model based on bivariate t copulas by deriving and implementing a reversible jump Markov chain Monte Carlo algorithm. However, the methodology is general and can be extended to any regular vine PCC and to all known bivariate copula families. The proposed approach considers model selection and estimation problems for PCCs simultaneously. The effectiveness of the developed algorithm is shown in simulations and its usefulness is illustrated in two real data applications.

### MSC:

 62F15 Bayesian inference 62H20 Measures of association (correlation, canonical correlation, etc.) 62H05 Characterization and structure theory for multivariate probability distributions; copulas 65C40 Numerical analysis or methods applied to Markov chains

### Keywords:

reversible jump Markov chain Monte Carlo; swap rates

Zbl 1165.60009
Full Text:

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