上证指数和沪深300指数序列的R/S实证分析

Rescaled Range Analysis of Time Series of Shanghai Composite Index and Hushen 300 Index

运用重标极差分析法(R/S分析法),分别研究上证综合指数和沪深300指数的日、月收益率数据序列以及开盘价、收盘价、最高价和最低价的股价时间序列的分形结构特征.给出了这些时间序列的Hurst指数、平均循环长度、相关指标和分形维数等分形特征量.实证分析结果表明,两个证券市场具有明显的分形结构,市场存在状态持续性,价格呈现周期性,4种形式的股价时间序列的分形维数具有近似同一性等特征.

The method of rescaled range analysis is used to study the fractal characteristics of Shanghai composite index and Hushen 300 index in this paper.Taking time series of daily and monthly return rates and four price sequences of stocks as study objects,we investigate the Hurst exponents,lengths of average cycle,relevant indicators and fractal dimensions of these sequences.The positive analysis shows that the two stock markets have the obvious fractal structure characteristics,and also have the sustainability of state,the periodicity of prices,and the approximate identity of fractal dimensions of four price sequences of stocks,etc.