Semiparametric Quantile Averaging in the Presence of High-Dimensional Predictors

Abstract

The paper proposes a method for forecasting conditional quantiles. In practice, one often does not know the structure of the underlying conditional quantile function. In addition, we may have a potentially large number of the predictors. Mainly intended for such cases, we introduce a flexible and practical framework based on penalized high-dimensional quantile averaging. In addition to prediction, we show that the proposed method can also serve as a valid predictor selector. We conduct extensive simulation experiments to asses its prediction and variable selection performances for nonlinear and linear model designs. In terms of predictor selection, the approach tends to select the true set of predictors with minimal false positives. With respect to prediction accuracy, the method competes well even with those benchmark/oracle methods that know one or more aspects of the underlying quantile regression model. To further illustrate the merit of the proposed method, we provide an application to the out-of-sample forecasting U.S. core inflation using a large set of monthly macroeconomic variables based on the recently developed FRED-MD database. The application offers several empirical findings.