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

Music City Center 

This paper considers an important finance problem, equity premium prediction, for which the mean regression as the standard approach can be problematic due to heteroscedasticity and heavy-tails of the error. We propose using penalized quantile regression to provide estimates of quantiles for equity premium. Many penalized quantile methods allow for the set of active variables to vary by quantile. We find increases the chances of causes crossing quantiles in the predictions. To mitigate this issue we propose using a group lasso to guarantee that the set of active variables is the same across all quantiles.

quantile regression