英文标题：
《Dynamical variety of shapes in financial multifractality》
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作者：
Stanis{\\l}aw Dro\\.zd\\.z, Rafa{\\l} Kowalski, Pawe{\\l} O\\\'swi\\c{e}cimka,
Rafa{\\l} Rak, Robert G\\c{e}barowski
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最新提交年份：
2018
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英文摘要：
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves to evaluation of whether or not a time series is multifractal and width of the resulting singularity spectrum is considered a measure of the degree of complexity involved. However, the character of the complexity of time series generated by the natural processes usually appears much more intricate than such a bare statement can reflect. As an example, based on the long-term records of S&P500 and NASDAQ - the two world leading stock market indices - the present study shows that they indeed develop the multifractal features, but these features evolve through a variety of shapes, most often strongly asymmetric, whose changes typically are correlated with the historically most significant events experienced by the world economy. Relating at the same time the index multifractal singularity spectra to those of the component stocks that form this index reflects the varying degree of correlations involved among the stocks.
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中文摘要：
多重分形的概念提供了一个强大的形式化工具，可以过滤掉复杂时间序列中许多最相关的特征。迄今为止，科学文献中的相关研究通常仅限于评估时间序列是否是多重分形的，而由此产生的奇异谱的宽度被视为所涉及的复杂程度的度量。然而，自然过程产生的时间序列的复杂性特征通常比这种简单的陈述所能反映的复杂得多。例如，根据标准普尔500指数和纳斯达克这两个世界领先的股票市场指数的长期记录，本研究表明，它们确实发展了多重分形特征，但这些特征通过各种形状演变，通常是强烈不对称的，其变化通常与世界经济经历的历史上最重要的事件相关。同时，指数多重分形奇异性谱与构成该指数的组成股票的多重分形奇异性谱相关联，反映了股票之间不同程度的相关性。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Physics 物理学
二级分类：Chaotic Dynamics 混沌动力学
分类描述：Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统，混沌，量子混沌，拓扑动力学，循环展开，湍流，传播
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一级分类：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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