D-vine copula based quantile regression

Abstract

Quantile regression, that is the prediction of conditional quantiles, has steadily gained importance in statistical modeling and financial applications. The authors introduce a new semiparametric quantile regression method based on sequentially fitting a likelihood optimal Dvine copula to given data resulting in highly flexible models with easily extractable conditional quantiles. As a subclass of regular vine copulas, D-vines enable the modeling of multivariate copulas in terms of bivariate building blocks, a so-called pair-copula construction (PCC). The proposed algorithm works fast and accurate even in high dimensions and incorporates an automatic variable selection by maximizing the conditional log-likelihood. Further, typical issues of quantile regression such as quantile crossing or transformations, interactions and collinearity of variables are automatically taken care of. In a simulation study the improved accuracy and saved computational time of the approach in comparison with established quantile regression methods is highlighted. An extensive financial application to international credit default swap (CDS) data including stress testing and Value-at-Risk (VaR) prediction demonstrates the usefulness of the proposed method.

Stress Testing German Industry Sectors: Results from a Vine Copula Based Quantile Regression

“…. , u d ) can be analytically expressed only using the pair-copulas of the D-vine (see Kraus and Czado 2017a). This is not possible for an arbitrary regular vine, which is why we use D-vine copulas.…”

“…Thus, the single stressed industry sector is a covariate in the regression model and all other sectors response variables. This is similar to the stress scenarios described in Kraus and Czado (2017a). The sector variables are evaluated on the copula scale.…”

“…In contrast to these studies, we apply extremal QR to investigate how crises (in the sense of higher PDs) in industry sectors are connected to other industry sectors. Above that, we circumvent the disadvantages of classical QR, namely the occurrence of so-called quantile-crossings and apply D-vine copula based quantile regression as recently advocated by Kraus and Czado (2017a), instead. Against this background, the outline of this work is as follows: Section 2 briefly reviews D-vines and D-vine copula based regression.…”

“…Next, we transform the differenced data to the copula scale by applying the probability integral transform using the kernel density estimators as marginal distribution functions (as described in detail in Kraus and Czado 2017a). The corresponding contour plots with standard normal margins and Kendall's τ values are displayed in Figure 3.…”

“…Kraus and Czado (2017a) propose an algorithm, which sequentially adds covariates to the D-vine that improve the model fit (measured in terms of the log-likelihood of the conditional density c V|U 1 ,...,U d (v|u 1 , . .…”