Pair-copula constructions for non-Gaussian DAG models

We propose a new type of multivariate statistical model that permits non-Gaussian distributions as well as the inclusion of conditional independence assumptions specified by a directed acyclic graph. These models feature a specific factorisation of the likelihood that is based on pair-copula constructions and hence involves only univariate distributions and bivariate copulas, of which some may be conditional. We demonstrate maximum-likelihood estimation of the parameters of such models and compare them to various competing models from the literature. A simulation study investigates the effects of model misspecification and highlights the need for non-Gaussian conditional independence models. The proposed methods are finally applied to modeling financial return data. The Canadian Journal of Statistics 40: 86109; 2012 (C) 2012 Statistical Society of Canada