  The realized GARCH framework is extended to incorporate the two-sided Weibull
distribution, for the purpose of volatility and tail risk forecasting in a
financial time series. Further, the realized range, as a competitor for
realized variance or daily returns, is employed in the realized GARCH
framework. Further, sub-sampling and scaling methods are applied to both the
realized range and realized variance, to help deal with inherent
micro-structure noise and inefficiency. An adaptive Bayesian Markov Chain Monte
Carlo method is developed and employed for estimation and forecasting, whose
properties are assessed and compared with maximum likelihood, via a simulation
study. Compared to a range of well-known parametric GARCH, GARCH with two-sided
Weibull distribution and realized GARCH models, tail risk forecasting results
across 7 market index return series and 2 individual assets clearly favor the
realized GARCH models incorporating two-sided Weibull distribution, especially
models employing the sub-sampled realized variance and sub-sampled realized
range, over a six year period that includes the global financial crisis.
