Quantile regression—the prediction of conditional quantiles—has steadily gained importance in statistical modeling. Using D-vine copulas, which are built from arbitrary bivariate (conditional) copulas, Kraus and Czado (2017) propose a novel approach for quantile regression, which automatically takes typical issues such as quantile crossing or transformations, interactions and collinearity of variables into account. Their algorithm is based on sequentially fitting a likelihood optimal D-vine copula to given data. D-vine copulas are not only a very flexible class of copulas, their construction principle further allows for easy extractability of the conditional quantiles. We build upon this work and develop methodologies for the general class of regular vine (R-vine) copulas. As opposed to D-vine copulas, where the underlying vine tree sequence follows a line structure, R-vine structures are not restricted and thus allow for even more complex dependencies between variables. We propose an algorithm that sequentially fits an optimal R-vine copula to given data. Due to the enormous amount of possible R-vine structures covariate selection via maximizing the conditional likelihood as suggested in Kraus and Czado (2017) is no longer feasible. We propose a partial correlation based selection approach, which computationally is significantly less demanding. The developed estimation and prediction approach will be presented along with an extensive simulation study to (1) show the good finite sample performance of the proposed methodology and (2) to compare the novel approach to benchmark models such as D-vine copula quantile regression and linear quantile regression. A real data example on DAX-stock returns will be discussed.
References: Kraus, D. and Czado, C.: D-vine copula based quantile regression. Computational Statistics and Data Analysis (110), 2017, 1-18.