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Multivariate copulas are commonly used in economics, finance and risk management. They allow for very flexible dependency structures, even though they are applied to transformed financial data after marginal time dependencies are removed. This is necessary to facilitate statistical parameter estimation. In this paper we consider a very flexible class of mixed C-vines, which allows the variables to be ordered according to their influence. Vines are build from bivariate copulas only and the term "mixed" refers to allowing the pair-copula family to be chosen individually for each term. In addition there are many C-vine structure specifications possible and therefore we propose a novel data driven sequential selection procedure, which selects both the C-vine structure and its attached pair-copula families with parameters. After the model selection ML estimation of the parameters is facilitated using the above found sequential estimates as starting values. An extensive simulation study shows a satisfactory performance of ML estimates in small samples. Finally an application involving US-exchange rates demonstrates the need for mixed C-vine models.

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.

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