关键词: FIGARCH（p.d.q）模型, 长记忆性

Abstract: The purpose of this paper is to represent and model the long memory property of Chinese stock returns series and compare it with foreign stock returns. The basic definition of long memory and FIGARCH model are given firstly, a Quasi-Maximum Likelihood Estimation (QMLE) and mixed algorithm are also applied. Through Monte-Carlo simulation, some of the most important results are reported. Then we compare the GRACH and IGARCH with FIGARCH processes, choose the one that best fit for the return series of Shanghai stock market and New York stock market respectively. The same aspect and the difference between these two market are analyzed, and some reasons are given.