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 L2-near-epoch dependent (NED) property to hold are established and the functional central limit theorems for ARCH(∞) models are proved. © 2017 The Korean Statistical Society, and Korean International Statistical Society.