英文标题：
《Joint multifractal analysis based on the partition function approach:
Analytical analysis, numerical simulation and empirical application》
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作者：
Wen-Jie Xie and Zhi-Qiang Jiang and Gao-Feng Gu and Xiong Xiong and
Wei-Xing Zhou
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最新提交年份：
2015
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英文摘要：
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive analytically several important properties. We apply the method numerically to binomial measures with multifractal cross correlations and bivariate fractional Brownian motions without multifractal cross correlations. For binomial multifractal measures, the explicit expressions of mass function, singularity strength and multifractal spectrum of the cross correlations are derived, which agree excellently with the numerical results. We also apply the method to stock market indexes and unveil intriguing multifractality in the cross correlations of index volatilities.
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中文摘要：
许多复杂系统都会产生多重分形时间序列，这些时间序列是长程互相关的。人们提出了许多方法来描述这些长程互相关的多重分形性质。然而，关于这些方法的几个重要问题还没有得到很好的理解，大多数方法只考虑一阶矩。我们研究了基于二阶矩配分函数的联合多重分形分析，它最初是为了研究流体场而发明的，并从解析角度推导了几个重要性质。我们将该方法数值应用于具有多重分形互相关的二项式测度和不具有多重分形互相关的二元分数布朗运动。对于二项式多重分形测度，导出了互相关的质量函数、奇异强度和多重分形谱的显式表达式，与数值结果非常吻合。我们还将该方法应用于股票市场指数，揭示了指数波动率交叉相关性中有趣的多重分形。
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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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