Functional central limit theorems for augmented GARCH(p,q) and FIGARCH processes

In this paper, we study the functional central limit theorem(FCLT) for the augmented GARCH process introduced by Duan (1997). We prove under proper moment assumptions that the process is geometrically L2-NED and then the FCLT holds. The fractional FCLT for FIGARCH processes is also considered. We examine the FCLT for the APGARCH, EGARCH and HYGARCH models as examples.