Bayesian Inference for Multivariate Copulas Using Pair-Copula Constructions

Abstract

This article provides a Bayesian analysis of pair-copula constructions (Aas et al., 2007 Insurance Math. Econom.) for modeling multivariate dependence structures. These constructions are based on bivariate t−copulas as building blocks and can model the nature of extremal events in bivariate margins individually. According to recent empirical studies (Fischer et al. (2007) and Berg and Aas (2007)) pair-copula constructions (PCC's) outperform many other multivariate copula constructions in fitting multivariate financial data. Parameter estimation in multivariate copulas is generally performed using maximum likelihood. However confidence intervals for parameters of PCC's are not easy to obtain and therefore statistical inference in these models has not been addressed so far. In this article we develop a Markov chain Monte Carlo (MCMC) algorithm which allows for interval estimation by means of credible intervals. Our MCMC algorithm can reveal unconditional as well as conditional independence in the data which can simplify resulting PCC's. In applications we consider Norwegian financial returns and Euro swap rates and are able to identify meaningful conditional independencies in both data sets. For the Norwegian financial returns data our findings support the view of Norway as a healthy economy, while for the Euro swap rates data they explain the nature of small twists in the yield curve.

Maximum likelihood estimation of mixed C-vines with application to exchange rates

“…These interval estimates are difficult to obtain in a ML setup. The mentioned papers in this paragraph are extensions of the Bayesian approach followed by Min and Czado (2010a), In the future we like to investigate the severeness of the restrictions imposed by the heuristic C-vine structure search. For this a discrepancy measure between the fitted C-vine structure and the true model has to be considered.…”

“…The advantage of this R-package is that mixed C-vine copula models can be used. Unlike Aas et al (2009), Min and Czado (2010a) or Nikoloulopoulos et al (2011) one is not limited to simple models with only one copula family for all pair-copulas in a C-vine PCC. In this paper we give a summary of our simulation study of the ML estimates in a fully specified C-vine.…”

Studying Volatility and Dependency of Chinese Outbound Tourism Demand in Singapore, Malaysia, and Thailand: A Vine Copula Approach

“…Bedford and Cooke [19] [8] expressed these constructions in terms of densities, and organized these constructions in a graphical way involving a sequence of nested trees, which are called regular vines. They also proposed two subclasses of PCC, which we call the C-vine and D-vine cop-ulas.…”

“…They also proposed two subclasses of PCC, which we call the C-vine and D-vine cop-ulas. Note that the C-vine and D-vine copulas have been widely used in finance asset returns and other data by many researchers, such as Aas et al [23], Min and Czado [19], and Czado [8]. For studying the dependence of outbound tourism demand in the three countries (SMT), we make use of the C-vine and D-vine copulas instead of the bivariate copula in the copula-GARCH model.…”

“…Then, we determine the required observations for C 23|1 and C 13|2 through the formulas (16)- (19). Thus, both C-vine and D-vine copulas can be estimated, and the Akaike information criterion (AIC) and Bayesian information criterion (BIC) can be calculated as well.…”