When MIDAS Meets LASSO : The Wisdom of Low-Frequency Variables in Forecasting Value-at-Risk and Expected Shortfall

It is well documented in the literature that the forecasts of Value-at-Risk (VaR) and Expected Shortfall (ES) can be improved by additional high-frequency information (i.e., realized volatility). However, existing framework provides no apparent way of integrating effective low-frequency signals. We propose a new framework for the joint estimation and forecasting of VaR and ES, which incorporates low-frequency macroeconomic and financial indicators into the quantile-based MIDAS model. Using an innovative machine-learning approach that maximizes the penalized Asymmetric Laplace (AL) likelihood function with an Adaptive Lasso penalty, the most informative variables are selected in a ``big data'' setting. The dynamic variable selection process enables the visualizing of the variable-selection evolution. In the empirical analysis, three variables (namely, realized volatility, term spread and housing starts) serve to the strongest predictors of future tail risk which provides novel statistical evidence of countercyclical tail risk. The out-of-sample backtesting results show that our method passes most backtests with relatively higher p-values and achieves the minimum loss in the joint forecasting of VaR and ES