Out-of-Sample Tests for Conditional Quantile Coverage - An Application to Growth-at-Risk
42 Pages Posted: 31 Aug 2020 Last revised: 12 Jul 2023
Date Written: June 30, 2023
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.
Keywords: Interval Prediction, Quantile Regression, Multiple Hypothesis Testing, Weak Moment Inequalities, Wild Bootstrap, Growth-at-Risk.
JEL Classification: C01, C12, C22, C53
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