  This paper develops a Bayesian framework for the realized exponential
generalized autoregressive conditional heteroskedasticity (realized EGARCH)
model, which can incorporate multiple realized volatility measures for the
modelling of a return series. The realized EGARCH model is extended by adopting
a standardized Student-t and a standardized skewed Student-t distribution for
the return equation. Different types of realized measures, such as sub-sampled
realized variance, sub-sampled realized range, and realized kernel, are
considered in the paper. The Bayesian Markov chain Monte Carlo (MCMC)
estimation employs the robust adaptive Metropolis algorithm (RAM) in the burn
in period and the standard random walk Metropolis in the sample period. The
Bayesian estimators show more favourable results than maximum likelihood
estimators in a simulation study. We test the proposed models with several
indices to forecast one-step-ahead Value at Risk (VaR) and Expected Shortfall
(ES) over a period of 1000 days. Rigorous tail risk forecast evaluations show
that the realized EGARCH models employing the standardized skewed Student-t
distribution and incorporating sub-sampled realized range are favored, compared
to a range of models.
