| Content | There are two commonly used hyperbolic GARCH processes, the FIGARCH and HYGARCH processes, in
modeling the long-range dependence in volatility. However, the FIGARCH process always has infinite
variance, and the HYGARCH model has a more complicated form. This paper builds a simple bridge
between a common GARCH model and an integrated GARCH model, and hence a new hyperbolic GARCH
model along the lines of FIGARCH models. The new model remedies the drawback of FIGARCH processes
by allowing the existence of finite variance as in HYGARCH models, while it has a form nearly as simple
as the FIGARCH model. Two inference tools, including the Gaussian QMLE and a portmanteau test for the
adequacy of the fitted model, are derived, and an easily implemented test for hyperbolic memory is also
constructed. Their finite sample performances are evaluated by simulation experiments, and an empirical
example gives further support to our new model. |
