金融中的有限规模效应与多重分形的构成 波动性

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摘要翻译：
许多金融变量表现出多重分形特性，这通常归因于概率分布(PDF)中的时间相关性和胖尾性的影响。基于多重分形分析的配分函数方法，证明了多重分形检测中存在明显的有限尺寸效应，有效多重分形是去除有限尺寸效应后的表观多重分形。我们发现有效多重分形可以进一步分解为两个分量，即PDF分量和非线性分量。参照正态分布，通过比较原始时间序列和具有正态分布且与原始数据具有相同线性和非线性相关性的替代数据的有效多重分形来确定PDF分量。本文以道琼斯工业平均指数1896年5月26日至2007年4月27日的日波动率数据为例，说明了本文的方法。大量的数值实验表明，只有当时间序列具有非线性时，时间序列才具有有效多重分形性，并且只有当时间序列具有非线性时，PDF才对有效多重分形性产生影响。我们的方法也可以应用于其他复杂系统中多重分形时间序列的多重分形性的判断和多重分形性分量的确定。
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英文标题：
《Finite-size effect and the components of multifractality in financial
  volatility》
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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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英文摘要：
  Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of multifractal analysis, we show that there is a marked finite-size effect in the detection of multifractality, and the effective multifractality is the apparent multifractality after removing the finite-size effect. We find that the effective multifractality can be further decomposed into two components, the PDF component and the nonlinearity component. Referring to the normal distribution, we can determine the PDF component by comparing the effective multifractality of the original time series and the surrogate data that have a normal distribution and keep the same linear and nonlinear correlations as the original data. We demonstrate our method by taking the daily volatility data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. Extensive numerical experiments show that a time series exhibits effective multifractality only if it possesses nonlinearity and the PDF has impact on the effective multifractality only when the time series possesses nonlinearity. Our method can also be applied to judge the presence of multifractality and determine its components of multifractal time series in other complex systems.
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PDF链接：
https://arxiv.org/pdf/0912.4782

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关键词：波动性 Multifractal distribution correlations Applications 序列 方法 multifractality PDF 有效