Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2001; 38(3): 495-504

Printed September 1, 2001

Copyright © The Korean Mathematical Society.

Strict stationarity and functional central limit theorem for ARCH/GARCH models

Oesook Lee and Jihyun Kim

Ewha Womans University, Ewha Womans University

Abstract

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In this paper we consider the (generalized) autoregressive models with conditional heteroscedasticity (ARCH/GARCH models). We will give conditions under which strict stationarity, ergodicity and the functional central limit theorem hold for the corresponding models.

Keywords: GARCH process, Markov chain, stationarity, ergodicity, functional central limit theorem

MSC numbers: 62M10, 60J10

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