中文摘要：

以沪深300指数作为股指时间序列的研究对象，首先运用分形插值法对股指序列的运行规律及波动特征进行分析和预测，并使用分形维数与Hurst指数定量刻画股指序列的波动复杂性及长程相关性。然后运用MF-DFA以及多重分形谱分析法，对股指序列的收益率作进一步的分析，结果表明，股指收益率序列具有多重分形性，并呈现出状态持续性或反持续性等特征。

英文摘要：

Taking the CSI 300 Index as the research objects of stock index time series, this paper first uses the fractal in- terpolation method to analysis and predict the fluctuation law and volatility characteristics of stock index time series, and fur- ther, using the fractal dimension and the Hurst index to depict quantitatively the characteristics of the fluctuation complexity and the long-range correlations of stock index series. Then we make a further multifractal analysis for the series of stock index returns by means of the MF-DFA and muhifractal spectrum analysis method. The results show that the series of stock index re- turns displays the long-range correlation and the muhifractal features.