  A semi-parametric joint Value-at-Risk (VaR) and Expected Shortfall (ES)
forecasting framework employing multiple realized measures is developed. The
proposed framework extends the realized exponential GARCH model to be
semi-parametrically estimated, via a joint loss function, whilst extending
existing quantile time series models to incorporate multiple realized measures.
A quasi-likelihood is built, employing the asymmetric Laplace distribution that
is directly linked to a joint loss function, which enables Bayesian inference
for the proposed model. An adaptive Markov Chain Monte Carlo method is used for
the model estimation. The empirical section evaluates the performance of the
proposed framework with six stock markets from January 2000 to June 2022,
covering the period of COVID-19. Three realized measures, including 5- minute
realized variance, bi-power variation, and realized kernel, are incorporated
and evaluated in the proposed framework. One-step-ahead VaR and ES forecasting
results of the proposed model are compared to a range of parametric and
semi-parametric models, lending support to the effectiveness of the proposed
framework.
