Penalized Averaging of Parametric and Non-Parametric Quantile Forecasts

We propose a hybrid penalized averaging for combining parametric and non-parametric quantile forecasts when faced with a large number of predictors. This approach goes beyond the usual practice of combining conditional mean forecasts from parametric time series models with only a few predictors. The hybrid methodology adopts the adaptive LASSO regularization to simultaneously reduce predictor dimension and obtain quantile forecasts. Several recent empirical studies have considered a large set of macroeconomic predictors and technical indicators with the goal of forecasting the S&P 500 equity risk premium. To illustrate the merit of the proposed approach, we extend the mean-based equity premium forecasting into the conditional quantile context. The application offers three main findings. First, combining parametric and non-parametric approaches adds quantile forecast accuracy over and above the constituent methods. Second, a handful of macroeconomic predictors are found to have systematic forecasting power. Third, different predictors are identified as important when considering lower, central and upper quantiles of the equity premium distribution.