中文摘要：

运用方差方法。重标极差方法（R／S）和消除趋势波动分析方法（DFA）对美国股市标准普尔500指数的收盘价进行分析。结果表明：此股票市场指数具有状态持续性特征及自相似特征。同时兼具混沌等非线性特征。通过这三种方法对同一股市进行分析更能全方位的诠释相关性在股票市场理论应用的必要性及可行性，并且对股票市场理论建模。预测和管控策略的制定及实施具有重要意义。

英文摘要：

We applied the variance method, R/S and DFA to analysis the closing values of the USA S＆P500 INDEX. The results showed that this stock market＇s index had the persistence, self-similarity and also the chaos nonlinear characteristics. Application the three methods to the same stock market can be more all-inclusively explained the necessity and feasibility for the theory application of the relation in the stock market, and also has important meaning for the stock market theoretical modelling, short forecast and making the control strategic plan.