标题： 金融市场中股价波动的 hierarchical 结构 显示英文标题

标题： Hierarchical structure of stock price fluctuations in financial markets

摘要： 由于金融市场和湍流采用了相同的定量方法，并且共享若干共同的风格化事实，因此它们被广泛比较。 本文应用了She-Leveque（SL）层次结构来解释流体湍流中速度波动偏离柯尔莫哥洛夫单分形标度的异常标度指数，研究并量化了金融市场上股票价格波动的层次结构。 因此，我们观察到一些有趣的结果：(i) 我们研究的所有股票价格波动中一般都存在与多重分形标度相关的层次结构。(ii) 描述SL层次结构的定量统计参数在发达金融市场和新兴市场之间存在显著差异。(iii) 对于高频股票价格波动，层次结构随不同的时间周期而变化。 所有这些结果为湍流和金融市场动力学提供了新颖的类比，并为深入理解金融市场的多重分形性提供了见解。 显示英文摘要

摘要： The financial market and turbulence have been broadly compared on account of the same quantitative methods and several common stylized facts they shared. In this paper, the She-Leveque (SL) hierarchy, proposed to explain the anomalous scaling exponents deviated from Kolmogorov monofractal scaling of the velocity fluctuation in fluid turbulence, is applied to study and quantify the hierarchical structure of stock price fluctuations in financial markets. We therefore observed certain interesting results: (i) The hierarchical structure related to multifractal scaling generally presents in all the stock price fluctuations we investigated. (ii) The quantitatively statistical parameters that describes SL hierarchy are different between developed financial markets and emerging ones, distinctively. (iii) For the high-frequency stock price fluctuation, the hierarchical structure varies with different time period. All these results provide a novelty analogy in turbulence and financial market dynamics and a insight to deeply understand the multifractality in financial markets.