Reduced form vector directional quantiles

In this paper, we develop a reduced form multivariate quantile model, using a directional quantile framework. The proposed model is the solution to a collection of directional quantile models for a fixed orthonormal basis, in which each component represents a directional quantile that corresponds to a particular endogenous variable. The model thus delivers a map from the space of exogenous variables (or the σ-field generated by the information available at a particular time) and a unit ball whose dimension is given by the number of endogenous variables, to the space of endogenous variables. The main effect of interest is that of exogenous variables on the vector of endogenous variables, which depends on a multivariate quantile index. An estimator is proposed, using quantile regression time series models, and we study its asymptotic properties. The estimator is then applied to study the interdependence among countries in the European sovereign bonds credit default swap market.