摘要翻译：
本文以道琼斯工业平均指数1896年5月26日至2007年4月27日的每日数据为例，对金融收益的经验多重分形性成分进行了系统的研究。收益的时间结构和厚尾分布是可能的影响因素。将原始收益率序列的多重分形谱与四种替代数据的多重分形谱进行了比较：（1）不含时间相关性但分布相同的洗牌数据；（2）去除任何非线性相关性但保持分布和线性相关性的替代数据；（3）用小值代替大正负收益率的替代数据；（4）保留时间相关性的替代胖尾分布生成的替代数据。我们发现这些因素都对多重分形谱有影响。我们还发现时间结构（线性或非线性）对多重分形谱的奇异点宽度影响较小，而胖尾对奇异点宽度影响较大，证实了前人的结果。此外，线性相关对多重分形谱仅有水平平移作用，距离近似等于其DFA标度指数与0.5之差。我们的方法也可以应用于其他金融或物理变量以及其他多重分形形式化。
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英文标题：
《The components of empirical multifractality in financial returns》
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作者：
Wei-Xing Zhou (ECUST)
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最新提交年份：
2009
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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：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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英文摘要：
  We perform a systematic investigation on the components of the empirical multifractality of financial returns using the daily data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. The temporal structure and fat-tailed distribution of the returns are considered as possible influence factors. The multifractal spectrum of the original return series is compared with those of four kinds of surrogate data: (1) shuffled data that contain no temporal correlation but have the same distribution, (2) surrogate data in which any nonlinear correlation is removed but the distribution and linear correlation are preserved, (3) surrogate data in which large positive and negative returns are replaced with small values, and (4) surrogate data generated from alternative fat-tailed distributions with the temporal correlation preserved. We find that all these factors have influence on the multifractal spectrum. We also find that the temporal structure (linear or nonlinear) has minor impact on the singularity width $\Delta\alpha$ of the multifractal spectrum while the fat tails have major impact on $\Delta\alpha$, which confirms the earlier results. In addition, the linear correlation is found to have only a horizontal translation effect on the multifractal spectrum in which the distance is approximately equal to the difference between its DFA scaling exponent and 0.5. Our method can also be applied to other financial or physical variables and other multifractal formalisms.
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PDF链接：
https://arxiv.org/pdf/0908.1089