Combining Value-at-Risk Forecasts Using Penalized Quantile Regressions

Penalized quantile regressions are proposed for the combination of Value-at-Risk forecasts. The primary reason for regularization of the quantile regression estimator with the elastic net, lasso and ridge penalties is multicollinearity among the standalone forecasts, which results in poor forecast performance of the non- regularized estimator due to unstable combination weights. This new approach is applied to combining the Value-at-Risk forecasts of a wide range of frequently used risk models for stocks comprising the Dow Jones Industrial Average Index. Within a thorough comparison analysis, the penalized quantile regressions perform better in terms of backtesting and tick losses than the standalone models and several competing forecast combination approaches. This is particularly evident during the global financial crisis of 2007-2008