Forecasting Value at Risk and Expected Shortfall with Mixed Data Sampling

Abstract

I propose applying the Mixed Data Sampling (MIDAS) framework to forecast Value at Risk (VaR) and Expected shortfall (ES). The new methods exploit the serial dependence in short-horizon returns to directly forecast the tail dynamics at the desired horizon. I perform a comprehensive comparison of out-of-sample VaR and ES forecasts with established models for a wide range of financial assets and backtests. The MIDAS-based models significantly outperform traditional GARCH-based forecasts and alternative conditional quantile specifications, especially at multi-day forecast horizons. My analysis advocates models featuring asymmetric conditional quantile and the use of Asymmetric Laplace density to jointly estimate VaR and ES.

Keywords: Value at Risk, Expected Shortfall, Mixed Data Sampling, Model Confidence Set, Backtesting

JEL Classification: G170, C180, C140