In the prediction of quantiles of daily Standard&Poor’s 500 (S&P 500) returns we consider how to use high-frequency 5-minute data. We examine methods that incorporate the high frequency information either indirectly, through combining forecasts (using forecasts generated from returns sampled...

In this paper we discuss how to compare various (possibly misspecified) density forecast models using the Kullback-Leibler information criterion (KLIC) of a candidate density forecast model with respect to the true density. The KLIC differential between a pair of competing models is the...