  Quantile regression, that is the prediction of conditional quantiles, has
steadily gained importance in statistical modeling and financial applications.
The authors introduce a new semiparametric quantile regression method based on
sequentially fitting a likelihood optimal D-vine copula to given data resulting
in highly flexible models with easily extractable conditional quantiles. As a
subclass of regular vine copulas, D-vines enable the modeling of multivariate
copulas in terms of bivariate building blocks, a so-called pair-copula
construction (PCC). The proposed algorithm works fast and accurate even in high
dimensions and incorporates an automatic variable selection by maximizing the
conditional log-likelihood. Further, typical issues of quantile regression such
as quantile crossing or transformations, interactions and collinearity of
variables are automatically taken care of. In a simulation study the improved
accuracy and saved computational time of the approach in comparison with
established quantile regression methods is highlighted. An extensive financial
application to international credit default swap (CDS) data including stress
testing and Value-at-Risk (VaR) prediction demonstrates the usefulness of the
proposed method.
