Optimally Harnessing Inter-Day and Intra-Day Information for Daily Value-at-Risk Prediction

We make use of quantile regression theory to obtain a combination of individual potentially-biased VaR forecasts that is optimal because it meets by construction ex post the correct out-of-sample conditional coverage criterion. This enables a Wald-type conditional quantile forecast encompassing test for any finite set of competing (semi/non)parametric models which can be nested. Two attractive properties of this backtesting approach are robustness to model risk and estimation uncertainty. We deploy the techniques to confront inter-day and high frequency intra-day VaR models for equity, FOREX, fixed income and commodity trading desks. Forecast combination of both types of models is especially warranted for more extreme-tail risks. Overall our empirical analysis supports the use of high frequency 5-minute price information for daily risk management