Conditional Quantile Coverage : an Application to Growth-at-Risk

This paper proposes tests for pairwise and multiple out-of-sample comparisons of parametric conditional quantile models. The tests rank the distance between actual and nominal conditional coverage w.r.t. the \textit{union} of information sets across models, for a given loss function. Our approach operates uniformly over a compact set of quantile ranks, thereby assessing models' relative forecast ability across different quantile subsets. We derive the limiting distribution and establish the first order validity of block bootstrap critical values. An empirical application to Growth-at-Risk (GaR) uncovers situations where a threshold quantile model improves over the standard linear quantile regression approach