Improving Quantile Forecasts via Realized Double Hysteretic GARCH Model in Stock Markets

This research introduces a realized double hysteretic GARCH (R-dhGARCH) model with a skew Student’s t distribution designed to improve quantile forecasts by allowing regime-switching in both volatility and measurement equations. The nonlinear model is flexible, accommodating both explosive persistence and high volatility in the first regime and effectively capturing extreme values within the volatility and measurement equations. Bayesian methods are proposed for estimating the unknown parameters of a target model while also forecasting value-at-risk (VaR) and expected shortfall (ES) simultaneously. An adaptive MCMC algorithm serves to sample from nonstandard posterior distributions. Illustrations of the proposed methods occur through a simulation study as well as from real examples. In the simulation study, parameter estimates and tail forecasts undergo evaluation. Daily data from four stock markets form the VaR and ES forecasts for a four-year out-of-sample period, including the COVID-19 pandemic period. Backtests, scoring functions, and Murphy diagrams help assess the models’ forecasts. The results show that the R-dhGARCH model outperforms other models in the U.S., Japan, and South Korea markets.