Bayesian quantile forecasting via the realized hysteretic GARCH model

This research introduces a new model, a realized hysteretic GARCH, that is similar to a three-regime nonlinear framework combined with daily returns and realized volatility. The setup allows the mean and volatility switching in a regime to be delayed when the hysteresis variable lies in a hysteresis zone. This nonlinear model presents explosive persistence and high volatility in Regime 1 in order to capture extreme cases. We employ the Bayesian Markov chain Monte Carlo (MCMC) procedure to estimate model parameters and to forecast volatility, value at risk (VaR), and expected shortfall (ES). A simulation study highlights the properties of the proposed MCMC methods, as well as their accuracy and satisfactory performance as quantile forecasting tools. We also consider two competing models, the realized GARCH and the realized threshold GARCH, for comparison and carry out Bayesian risk forecasting via predictive distributions on four stock markets. The out-of-sample period covers the recent 4 years by a rolling window approach and includes the COVID-19 pandemic period. Among the realized models, the realized hysteretic GARCH model outperforms at the 1% level in terms of violation rates and backtests.