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

Abstract

Abstract We propose a new framework for the joint estimation and forecasting of Value-at-Risk (VaR) and Expected Shortfall (ES) that integrates low-frequency variables. By maximizing the Asymmetric Laplace likelihood function with an Adaptive Lasso penalty, the most informative variables are selected on a rolling-window basis. In the empirical analysis, realized volatility, term spread, and housing starts serve as the strongest predictors of future tail risk. The out-of-sample backtesting results demonstrate that our method significantly outperforms other benchmarks, and achieves minimum loss in the joint forecasting of both the one-day-ahead and multi-day-ahead extreme S&P500 VaR and ES.