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.
- Augmented GARCH
- Fractional FCLT
- Functional central limit theorem