  Quantile regression is a field with steadily growing importance in
statistical modeling. It is a complementary method to linear regression, since
computing a range of conditional quantile functions provides a more accurate
modelling of the stochastic relationship among variables, especially in the
tails. We introduce a non-restrictive and highly flexible nonparametric
quantile regression approach based on C- and D-vine copulas. Vine copulas allow
for separate modeling of marginal distributions and the dependence structure in
the data, and can be expressed through a graph theoretical model given by a
sequence of trees. This way we obtain a quantile regression model, that
overcomes typical issues of quantile regression such as quantile crossings or
collinearity, the need for transformations and interactions of variables. Our
approach incorporates a two-step ahead ordering of variables, by maximizing the
conditional log-likelihood of the tree sequence, while taking into account the
next two tree levels. Further, we show that the nonparametric conditional
quantile estimator is consistent. The performance of the proposed methods is
evaluated in both low- and high-dimensional settings using simulated and real
world data. The results support the superior prediction ability of the proposed
models.
