# Functional central limit theorems for ARCH(∞) models

• Choi, Seunghee (Department of Statistics, Ewha Womans University) ;
• Lee, Oesook (Department of Statistics, Ewha Womans University)
• Accepted : 2017.09.14
• Published : 2017.09.30

#### Abstract

In this paper, we study ARCH(${\infty}$) 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(${\infty}$) models are proved.

#### Acknowledgement

Supported by : NRF

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