Quantile Predictions for Equity Premium using Penalized Quantile Regression with Consistent Variable Selection across Multiple Quantiles

TL;DR

This paper introduces a novel penalized quantile regression method for equity premium prediction that enforces consistent variable selection across all quantiles, improving interpretability and predictive performance.

Contribution

It proposes a group penalty approach for simultaneous quantile estimation, ensuring variable selection consistency and addressing crossing quantile issues in equity premium modeling.

Findings

The method outperforms benchmark models in empirical tests.

Predictor relationships vary across quantiles, revealing new insights.

Simulation studies confirm the approach's effectiveness.

Abstract

This paper considers equity premium prediction, for which mean regression can be problematic due to heteroscedasticity and heavy-tails of the error. We show advantages of quantile predictions using a novel penalized quantile regression that offers a model for a full spectrum analysis on the equity premium distribution. To enhance model interpretability and address the well-known issue of crossing quantile predictions in quantile regression, we propose a model that enforces the selection of a common set of variables across all quantiles. Such a selection consistency is achieved by simultaneously estimating all quantiles with a group penalty that ensures sparsity pattern is the same for all quantiles. Consistency results are provided that allow the number of predictors to increase with the sample size. A Huberized quantile loss function and an augmented data approach are implemented for computational efficiency. Simulation studies show the effectiveness of the proposed approach. Empirical results show that the proposed method outperforms several benchmark methods. Moreover, we find some important predictors reverse their relationship to the excess return from lower to upper quantiles, potentially offering interesting insights to the domain experts. Our proposed method can be applied to other fields.