Bayesian tail-risk forecasting using realized GARCH

A realized generalized autoregressive conditional heteroskedastic (GARCH) model is developed within a Bayesian framework for the purpose of forecasting value at risk and conditional value at risk. Student-t and skewed-t return distributions are combined with Gaussian and student-t distributions in the measurement equation to forecast tail risk in eight international equity index markets over a 4-year period. Three realized measures are considered within this framework. A Bayesian estimator is developed that compares favourably, in simulations, with maximum likelihood, both in estimation and forecasting. The realized GARCH models show a marked improvement compared with ordinary GARCH for both value-at-risk and conditional value-at-risk forecasting. This improvement is consistent across a variety of data and choice of distributions. Realized GARCH models incorporating a skewed student-t distribution for returns are favoured overall, with the choice of measurement equation error distribution and realized measure being of lesser importance. (C) 2017 John Wiley & Sons, Ltd.