  In this paper, we propose the realized Hyperbolic GARCH model for the
joint-dynamics of lowfrequency returns and realized measures that generalizes
the realized GARCH model of Hansen et al.(2012) as well as the FLoGARCH model
introduced by Vander Elst (2015). This model is sufficiently flexible to
capture both long memory and asymmetries related to leverage effects. In
addition, we will study the strictly and weak stationarity conditions of the
model. To evaluate its performance, experimental simulations, using the Monte
Carlo method, are made to forecast the Value at Risk (VaR) and the Expected
Shortfall (ES). These simulation studies show that for ES and VaR forecasting,
the realized Hyperbolic GARCH (RHYGARCH-GG) model with Gaussian-Gaussian errors
provide more adequate estimates than the realized Hyperbolic GARCH model with
student- Gaussian errors.
