Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine

Abstract

Flexible multivariate distributions are needed in many areas. The popular multivariate Gaussian distribution is however very restrictive and cannot account for features like asymmetry and heavy tails. Therefore dependence modeling using copulas is nowadays very common to account for such patterns. The use of copulas is however challenging in higher dimensions, where standard multivariate copulas suffer from rather inflexible structures. Vine copulas overcome such limitations and are able to model complex dependency patterns by benefiting from the rich variety of bivariate copulas as building blocks. This article presents the R package CDVine which provides functions and tools for statistical inference of canonical vine (C-vine) and D-vine copulas. It contains tools for bivariate exploratory data analysis and for bivariate copula selection as well as for selection of pair-copula families in a vine. Models can be estimated either sequentially or by joint maximum likelihood estimation. Sampling algorithms and graphical methods are also included.