Quantile regression is a field with growing importance for statistical modeling. It has a broad range of applications and it emerged as a complementary method to linear regression in many fields. Ever since the formal definition for quantile regression has been formulated, by Koenker and Bassett Jr (1978), there have been many attempts to improve this methods shortfalls. The occurrence of quantile crossings and the linearity assumption are just a few disadvantages of linear quantile regression. One of the ideas how to overcome such shortfalls, is to use vine copula based quantile regression. Vine-copulas allow highly flexible modeling of high-dimensional dependence structures. The first work in this field by Kraus and Czado (2017), introduced D-vine quantile regression for the subclass of D-vines. The idea how to build the D-vine copula is based on the maximal improvement of the conditional log likelihood in the next tree. Our first goal is to extend this method to the subclass of C-vines, so that more flexible dependence structures can be modeled. The next step is to introduce new algorithms for both D-vine and C-vine copulas, where we look on the next two trees for the maximal improvement in the conditional log likelihood. Furthermore, an additional goal is to be able to use these algorithms on big data sets, and thus, we introduce some modifications in our two-step ahead algorithm in order to reduce the computational complexity. At the end, we try to examine the performance of the algorithms through an extensive simulation study, where we compare the proposed algorithms based on several performance measures which include, among others, the out of sample mean square error, conditional log likelihood and computational time.     «

Quantile regression is a field with growing importance for statistical modeling. It has a broad range of applications and it emerged as a complementary method to linear regression in many fields. Ever since the formal definition for quantile regression has been formulated, by Koenker and Bassett Jr (1978), there have been many attempts to improve this methods shortfalls. The occurrence of quantile crossings and the linearity assumption are just a few disadvantages of linear quantile regression. One...     »