## Bayesian Analysis

### Bayesian Model Selection of Regular Vine Copulas

#### Abstract

Regular vine copulas are a flexible class of dependence models, but Bayesian methodology for model selection and inference is not yet fully developed. We propose sparsity-inducing but otherwise non-informative priors, and present novel proposals to enable reversible jump Markov chain Monte Carlo posterior simulation for Bayesian model selection and inference. Our method is the first to jointly estimate the posterior distribution of all trees of a regular vine copula. This represents a substantial improvement over existing frequentist and Bayesian strategies, which can only select one tree at a time and are known to induce bias. A simulation study demonstrates the feasibility of our strategy and shows that it combines superior selection and reduced computation time compared to Bayesian tree-by-tree selection. In a real data example, we forecast the daily expected tail loss of a portfolio of nine exchange-traded funds using a fully Bayesian multivariate dynamic model built around Bayesian regular vine copulas to illustrate our model’s viability for financial analysis and risk estimation.

#### Article information

Source
Bayesian Anal., Volume 13, Number 4 (2018), 1111-1135.

Dates
First available in Project Euclid: 29 December 2017

https://projecteuclid.org/euclid.ba/1514516431

Digital Object Identifier
doi:10.1214/17-BA1089

Mathematical Reviews number (MathSciNet)
MR3855365

Zentralblatt MATH identifier
06989978

#### Citation

Gruber, Lutz F.; Czado, Claudia. Bayesian Model Selection of Regular Vine Copulas. Bayesian Anal. 13 (2018), no. 4, 1111--1135. doi:10.1214/17-BA1089. https://projecteuclid.org/euclid.ba/1514516431

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