STATIONARITY OF SQUARES SEQUENCES FROM
ARCH(1)

Zhiqiang Zhang (P. R. China), Riquan Zhang (P. R. China) and Jingyan Feng (P. R. China)

Received November 9, 2007

Abstract

In this paper, the stationarity of squares sequences from ARCH(1) is discussed and the asymptotic properties of squares sequences from ARCH(1) that the sequences converge to a Brownian motion in distribution, and are convergent in almost sure and in mean square are given under some mild conditions.

Keywords and phrases: ARCH, converges in distribution, Brownian motion, almost sure convergence, mean square convergence.