A Bayesian realized threshold measurement GARCH framework for financial tail risk forecasting

This paper proposes an innovative threshold measurement equation to be employed in a Realized-Generalized Autoregressive Conditional Heteroskedastic (GARCH) framework. The proposed framework incorporates a nonlinear threshold regression specification to consider the leverage effect and model the contemporaneous dependence between the observed realized measure and hidden volatility. A Bayesian Markov chain Monte Carlo method is adapted and employed for model estimation, with its validity assessed via a simulation study. The validity of incorporating the proposed measurement equation in Realized-GARCH type models is evaluated via an empirical study, forecasting the 1% and 2.5% Value-at-Risk and expected shortfall on six market indices with two different out-of-sample sizes. The proposed framework is shown to be capable of producing competitive tail risk forecasting results in comparison with the GARCH and Realized-GARCH type models.