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The realized GARCH framework is extended to incorporate the two-sided Weibulldistribution, for the purpose of volatility and tail risk forecasting in afinancial time series. Further, the realized range, as a competitor forrealized variance or daily returns, is employed in the realized GARCHframework. Further, sub-sampling and scaling methods are applied to both therealized range and realized variance, to help deal with inherentmicro-structure noise and inefficiency. An adaptive Bayesian Markov Chain MonteCarlo method is developed and employed for estimation and forecasting, whoseproperties are assessed and compared with maximum likelihood, via a simulationstudy. Compared to a range of well-known parametric GARCH, GARCH with two-sidedWeibull distribution and realized GARCH models, tail risk forecasting resultsacross 7 market index return series and 2 individual assets clearly favor therealized GARCH models incorporating two-sided Weibull distribution, especiallymodels employing the sub-sampled realized variance and sub-sampled realizedrange, over a six year period that includes the global financial crisis.

Bayesian Realized-GARCH Models for Financial Tail Risk Forecasting Incorporating Two-sided Weibull Distribution