As the prediction of conditional quantiles plays an important role in various fields of economics (e.g. value at risk in finance), quantile regression has steadily gained importance in statistical modeling. Since the introduction of linear quantile regression, which models the linear conditional quantile function using regression coefficients, multiple methods have been developed aiming to improve the model's shortfalls, such as the linearity assumption and quantile crossing. D-vine copula based quantile regression was the first quantile regression method that estimates the conditional quantile function using vine copulas. As the method's name indicates, D-vine copula based quantile regression is restricted to the class of D-vine copulas. The goal of this thesis is to develop a regular vine (R-vine) copula based quantile regression method. That means we want to sequentially fit an optimal R-vine copula to given copula data and estimate the conditional quantile function of a response given a set of covariates using the conditional distribution described by the estimated R-vine copula. Intuitively one might think of a one to one extension of the D-vine quantile regression approach to the more general class of regular vine copulas. However, since already for small numbers of covariates the class of R-vine copulas exceeds the class of D-vine copulas enormously, it would require too much computational effort to determine the optimal R-vines by conditional likelihood arguments as done in D-vine quantile regression. Therefore, we propose a partial correlation based approach to select the sequence on how the potential covariates enter the R-vine copula and use additional criteria in order to decrease the number of R-vine tree sequence candidates. In order to enable the reader to understand the terms and notations used in our methods, we present common, as well as method-specific concepts related to R-vine copulas. After introducing and illustrating our methods, we compare our approach to the benchmarks D-vine copula based quantile regression and linear quantile regression within a simulation study and apply our method to the abalone data set aiming to predict the weight of female abalones.      «

As the prediction of conditional quantiles plays an important role in various fields of economics (e.g. value at risk in finance), quantile regression has steadily gained importance in statistical modeling. Since the introduction of linear quantile regression, which models the linear conditional quantile function using regression coefficients, multiple methods have been developed aiming to improve the model's shortfalls, such as the linearity assumption and quantile crossing. D-vine copula based...     »