Regular vine distributions which constitute a flexible class of multivariate dependence models are discussed. Since multivariate copulae constructed through pair-copula decompositions were introduced to the statistical community, interest in these models has been growing steadily and they are finding successful applications in various fields. Research so far has however been concentrating on so-called canonical and D-vine copulae, which are more restrictive cases of regular vine copulae. It is shown how to evaluate the density of arbitrary regular vine specifications. This opens the vine copula methodology to the flexible modeling of complex dependencies even in larger dimensions. In this regard, a new automated model selection and estimation technique based on graph theoretical considerations is presented. This comprehensive search strategy is evaluated in a large simulation study and applied to a 16-dimensional financial data set of international equity, fixed income and commodity indices which were observed over the last decade, in particular during the recent financial crisis. The analysis provides economically well interpretable results and interesting insights into the dependence structure among these indices.

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.

Using only bivariate copulas as building blocks, regular vine copulas constitute a flexible class of high‐dimensional dependency models. However, the flexibility comes along with an exponentially increasing complexity in larger dimensions. In order to counteract this problem, we propose using statistical model selection techniques to either truncate or simplify a regular vine copula. As a special case, we consider the simplification of a canonical vine copula using a multivariate copula as previously treated by Heinen & Valdesogo (2009) and Valdesogo (2009). We validate the proposed approaches by extensive simulation studies and use them to investigate a 19‐dimensional financial data set of Norwegian and international market variables. The Canadian Journal of Statistics 40: 68–85; 2012 © 2012 Statistical Society of Canada

The demand for an accurate financial risk management involving larger numbers of assets is strong not only in view of the financial crisis of 2007-2009. Especially dependencies among assets have not been captured adequately. While standard multivariate copulas have added some flexibility, this flexibility is insufficient in higher dimensional applications. Vine copulas can fill this gap by benefiting from the rich class of existing bivariate parametric copula families. Exploiting this in combination with GARCH models for the margins, we develop a regular vine copula based factor model for asset returns, the Regular Vine Market Sector model, which is motivated by the classical CAPM and shown to be superior to the CAVA model proposed by Heinen and Valdesogo (2009). The model can also be used to separate the systematic and idiosyncratic risk of specific stocks, and we explicitly discuss how vine copula models can be employed for active and passive portfolio management. In particular, Value-at-Risk forecasting and asset allocation are treated in detail. All developed models and methods are used to analyze the Euro Stoxx 50 index, a major market indicator for the Eurozone. Relevant benchmark models such as the popular DCC model and the common Student's t copula are taken into account.

No abstract