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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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This paper focuses on an extension of zero-inflated generalized Poisson (ZIGP) regression models for count data. We discuss generalized Poisson (GP) models where dispersion is modelled by an additional model parameter. Moreover, zero-inflated models in which overdispersion is assumed to be caused by an excessive number of zeros are discussed. In addition to ZIGP regression introduced by Famoye and Singh (2003), we now allow for regression on the overdispersion and zero-inflation parameters. Consequently, we propose tools for an exploratory data analysis on the dispersion and zero-inflation level. An application dealing with outsourcing of patent filing processes will be used to compare these nonnested models. The model parameters are fitted by maximum likelihood. Asymptotic normality of the ML estimates in this non-exponential setting is proven. Standard errors are estimated using the asymptotic normality of the estimates. Appropriate exploratory data analysis tools are developed. Also, a model comparison using AIC statistics and Vuong tests (see Vuong (1989)) is carried out. For the given data, our extended ZIGP regression model will prove to be superior over GP and ZIP models and even ZIGP models with constant overall dispersion and zero-inflation parameters demonstrating the usefulness of our proposed extensions.

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In recent years analyses of dependence structures using copulas have become more popular than the standard correlation analysis. Starting from Aas et al. (2009) 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. In this paper 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. The Canadian Journal of Statistics 39: 239–258; 2011 © 2011 Statistical Society of Canada