Abstract: Reviewing the history is aimed to predict the future. History contains the thread and the inherent law of the development of a thing. Can investors make investment decisions and predict the future trend through the analysis of stock market history? In this paper, taking Shanghai Composite Index, Shenzhen Compositional Index, Nikkei 225 and S&P 500 index as the samples, the dynamic estimation method is used to analysis the time-varying characteristics of long memory in the stock market, and the value of historical information is explored;and using the modified R/S method and LW estimates, two more novelty correction LW estimation method are employed for comparison, and the research of stock market long memory characteristics is expected to promoted. The empirical results show that, although the specific values are not exactly the same from different methods, but the same conclusions about the stock market long memory can be obtained;the stock return series did not have significantly long memory in the whole sample interval, but with extreme events, such as the 1990's real estate crisis in the Japanese, the Asian financial crisis in 1997, the U.S. financial crisis in 2008 and so on, return series exhibit a significant correlation, which inflect the time-varying characteristics of stock market long memory, and the extreme risk can be avoided by analysis historical information. Without regarding to the differences of cultural, economic and social background, this paper researches the China, Asia and globally representative stock index, and discusses the long memory characteristics of return series. An empirical evidence is provided for comprehensive understanding of the effective market hypothesis theory, and a support for risk management use the market's history information is also provided.

Key words: anti-persistence, long memory, LW estimates, extreme events