Abstract
This paper proposes tests for out-of-sample comparisons of interval forecasts based on parametric
conditional quantile models. The tests rank the distance between actual and nominal conditional
coverage with respect to the set of conditioning variables from all models, for a given loss function.
We propose a pairwise test to compare two models for a single predictive interval. The set-up is
then extended to a comparison across multiple models and/or intervals. The limiting distribution
varies depending on whether models are strictly non-nested or overlapping. In the latter case,
degeneracy may occur. We establish the asymptotic validity of wild bootstrap based critical
values across all cases. An empirical application to Growth-at-Risk (GaR) uncovers situations in
which a richer set of financial indicators are found to outperform a commonly-used benchmark
model when predicting downside risk to economic activity.