Penalized Averaging of Quantile Forecasts from GARCH Models with Many Exogenous Predictors

Abstract

This study explores the multi-step ahead forecasting performance of a so-called hybrid conditional quantile method, which combines relevant conditional quantile forecasts from parametric and semiparametric methods. The focus is on lower (left) and upper (right) tail quantiles of the conditional distribution of the response variable. First, we evaluate and compare out-of-sample conditional quantile forecasts obtained from a hybrid method and from five non-hybrid methods, employing a large data set of exogenous predictors generated by various GARCH model specifications. Second, we compare the accuracy of these methods by calculating conditional quantile forecasts for the risk premium of the monthly S&P 500 index, using a data set of macroeconomic predictors. Monte Carlo and empirical application results indicate that the hybrid forecasting provides more accurate quantile forecasts than non-hybrid methods. The success of the hybrid method is most prominent when compared with results obtained by a simple equal-weighted combination of quantile forecasts.