ON ALMOST SURE LIMIT THEOREM AND STRONG LAW OF LARGE NUMBERS FOR SQUARES SEQUENCE FROM ARCH(1)

Yang Shi (P. R. China), Zhiqiang Zhang (P. R. China) and Riquan Zhang (P. R. China)

Received May 26, 2008

Abstract

In this paper, we prove an almost sure limit theorem and give the rate of convergence in the strong law of large numbers for the squares sequence from ARCH(1) under some mild conditions.

Keywords and phrases: ARCH, almost sure limit theorem, rate of convergence, strong law of large numbers, positive quadrant dependence.