上海股票市场的标度特征

On the Scaling Characteristics of Shanghai Stock Market

在分形理论的基础上，以上海股票市场为例，对1990年～2003年间上证综合指数的标度特征进行了实证研究．首先通过重标极差分析方法及V统计分析方法对上证综指的标度不变性进行了确认．其次，通过多重分形标度分析的方法进一步研究了上证综指时间序列的多重分形标度特征．实证结果表明，上海股票市场显示出不同时间标度上股票收益时间序列的持久性，而且表现出超过一年半时间的平均非周期性循环；另外，多重分形标度分析的方法不但能够确认标度不变性，而且能够说明金融时间序列中概率分布的标度变化，这对描述时间序列的变化规律具有现实意义．

Taking the Shanghai stock market as example, scaling characteristics of Shanghai composite index （1990-2003） are studied on the basis of fractal theory. Rescaled range analysis and V statistic models are applied to the practical test to confirm the scaling invariance of Shanghai composite index. Then, the muhifractal scale characteristics of the time series were roughly identified through muhifractal scale analysis. It was found that the time series of the stock return show persistence property in different time scales and there is a non-periodic cycle in the time series with an average frequency about one and a half years. In addition, the method of muhifractal can not only identify the scaling invariance but also explain the scaling behavior of the prohability distributions in financial time series, which is of actual importance to describing more accurately the variation of time series.