英文标题：
《Detrended Cross-Correlation Analysis Consistently Extended to
  Multifractality》
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作者：
Pawe{\\l} O\\\'swi\\c{e}cimka, Stanis{\\l}aw Dro\\.zd\\.z, Marcin Forczek,
  Stanis{\\l}aw Jadach, Jaros{\\l}aw Kwapie\\\'n
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最新提交年份：
2014
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英文摘要：
  We propose a novel algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that constitutes a consistent extension of the Detrended Cross-Correlation Analysis (DCCA) and is able to properly identify and quantify subtle characteristics of multifractal cross-correlations between two time series. Our motivation for introducing this algorithm is that the already existing methods like MF-DXA have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross-correlations when there are none. The principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments. Furthermore, we present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust and selective tool at the same time, and therefore allows for a reliable quantification of the cross-correlative structure of analyzed processes. In particular, it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized Hurst exponent and the multifractal scaling parameter $\\lambda_q$. This relation provides information about character of potential multifractality in cross-correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far. By using examples of time series from stock market, we show that financial fluctuations typically cross-correlate multifractally only for relatively large fluctuations, whereas small fluctuations remain mutually independent even at maximum of such cross-correlations. Finally, we indicate possible utility of MFCCA to study effects of the time-lagged cross-correlations.
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中文摘要：
我们提出了一种新算法——多重分形互相关分析（MFCCA）——它是去趋势互相关分析（DCCA）的一致扩展，能够正确识别和量化两个时间序列之间多重分形互相关的细微特征。我们引入该算法的动机是，现有的方法，如MF-DXA，对于大多数描述复杂自然过程的信号，充其量也有严重的局限性，并且在没有多重分形互相关的情况下，往往指示多重分形互相关。当前扩展的主要部分是将涨落的符号适当地并入它们的广义矩。此外，我们对模型分形随机过程以及真实信号进行了广泛的分析，并表明MFCCA同时是一种稳健和选择性的工具，因此可以可靠地量化分析过程的交叉相关结构。特别是，它可以识别多重分形标度的边界，并分析广义赫斯特指数和多重分形标度参数$\\lambda_q$之间的关系。这种关系提供了有关互相关中潜在多重分形特征的信息，因此能够比迄今为止任何其他相关方法更深入地了解所分析过程的动力学。通过使用股票市场的时间序列的例子，我们表明，金融波动通常仅在相对较大的波动中以多重分形的方式相互关联，而小的波动即使在这种相互关联的最大值下仍然是相互独立的。最后，我们指出了MFCCA在研究时滞互相关效应方面的可能用途。
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分类信息：

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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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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