Functional central limit theorems for ARCH(∞) models

Abstract

In this paper, we study ARCH(∞) models with either geometrically decaying coefficients or hyperbolically decaying coefficients. Most popular autoregressive conditional heteroscedasticity (ARCH)-type models such as various modified generalized ARCH (GARCH) (p, q), fractionally integrated GARCH (FIGARCH), and hyperbolic GARCH (HYGARCH). can be expressed as one of these cases. Sufficient conditions for L 2 -near-epoch dependent (NED) property to hold are established and the functional central limit theorems for ARCH(∞) models are proved.