Abstract

We propose new models to directly forecast Value at Risk (VaR) and Expected shortfall (ES) with the mixed

data sampling (MIDAS)framework. The new method applies different MIDAS specifications for the conditional quantile of return at various return horizons using the high-frequency (daily) data. The conditional VaR and ES are jointly estimated either by maximum likelihood of Asymmetric Laplace distribution or by combining MIDAS quantile regression and extreme value theory. Using three indexes of different asset classes and an extensive batery of back-testing techniques, we find that the proposed approach provides competitive out-of-sample Var and ES forecasts with established benchmark methods. The MIDAS-based forecasts with Asymmetric Laplace distribution are consistently amongst the best performing models across asset classes,probability levels and return horizons.