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作者将多重分形分析的三种方法(配分函数分析法、奇异谱分析法和多重分形趋势消除波动分析法)应用于我国上海证券市场在过去七年中的收盘指数序列,分析了不同时间标度对多重分形特性的影响.结果表明:上海证券市场具有弱多重分形特征,标度不变性达到六个数量级;多重分形的形状不随时间标度的改变而改变,但其强度随标度的减小而减弱;随着配分阶数的增大,多重分形随之增强,奇异谱曲线越来越粗糙,广义赫斯特指数逐渐减小.这些结果为进一步研究证券市场价格变化的动力学机理提供了坚实的实证基础.
The author applies the three methods of multifractal analysis (partition function analysis, singular spectrum analysis and multifractal trend elimination volatility analysis) to the closing index series of Shanghai stock market in China in the past seven years, and analyzes different time scales On the multifractal characteristics.The results show that the Shanghai stock market has weak multifractal characteristics and the scale invariance reaches six orders of magnitude.The shape of multifractal does not change with the time scale change but its intensity decreases with the decrease of scale And the multi-fractal increases with the increase of the order of fractional numbers, the curve of the singular spectrum becomes more and more rough, and the generalized Hearst index decreases gradually. These results provide the basis for further study on the kinetic mechanism of price changes in the stock market A solid empirical basis.