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

Abstract

AbstractThis 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.