D-vine Generalized Additive Model copula-based quantile regression with application to ensemble postprocessing

Abstract The D-vine copula-based quantile regression (DVQR) is a powerful tool for weather forecasting, as it is able to select informative predictor variables from a large set and takes account of nonlinear relationships among them. However, DVQR shows in its current form a lack in adaptively modelling strongly varying effects among variables, such as temporal and/or spatial effects. Consequently, we propose an extension of the current DVQR, where we specify the parameters of the bivariate copulas in the D-vine copula through Kendall’s τ to which additional covariates are linked. The parameterization of the correlation parameter allows generalized additive models (GAMs) to incorporate, e.g. linear, nonlinear, and spatial effects as well as interactions. The new method is called GAM-DVQR, and its performance is illustrated in a case study on postprocessing 2 m surface temperature ensemble weather forecasts. We investigate constant as well as time-dependent Kendall’s τ correlation models. The results indicate that the GAM-DVQR models are able to identify time-dependent correlations and significantly outperform state-of-the-art postprocessing methods. Furthermore, the introduced temporal parameterization allows a more economical and faster model estimation in comparison to DVQR using a sliding training window. To complement this article, we provide an R-package for our method called gamvinereg.