2017-10-12 - This paper develops a reduced form multivariate quantile autoregressive model, using a directional quantile framework. The proposed model is the solution to a collection of directional quantile models for 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 sigma 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. This model is used for forecasting procedures and to construct quantile impulse-response functions that explore dynamic heterogeneity in the response of endogenous variables to shocks. The model is then applied to a three-variable macroeconomic model (output gap, inflation, Fed Funds rate) for the U.S. for the period 1980q1-2010q1. This new analysis reveal important asymmetries in extreme events.