英文标题：
《Detrended fluctuation analysis made flexible to detect range of
  cross-correlated fluctuations》
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作者：
Jaroslaw Kwapien, Pawel Oswiecimka, Stanislaw Drozdz
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最新提交年份：
2015
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英文摘要：
  The detrended cross-correlation coefficient $\\rho_{\\rm DCCA}$ has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, non-stationary time series. It is based on the detrended cross-correlation and detrended fluctuation analyses (DCCA and DFA, respectively) and can be viewed as an analogue of the Pearson coefficient in the case of the fluctuation analysis. The coefficient $\\rho_{\\rm DCCA}$ works well in many practical situations but by construction its applicability is limited to detection of whether two signals are generally cross-correlated, without possibility to obtain information on the amplitude of fluctuations that are responsible for those cross-correlations. In order to introduce some related flexibility, here we propose an extension of $\\rho_{\\rm DCCA}$ that exploits the multifractal versions of DFA and DCCA: MFDFA and MFCCA, respectively. The resulting new coefficient $\\rho_q$ not only is able to quantify the strength of correlations, but also it allows one to identify the range of detrended fluctuation amplitudes that are correlated in two signals under study. We show how the coefficient $\\rho_q$ works in practical situations by applying it to stochastic time series representing processes with long memory: autoregressive and multiplicative ones. Such processes are often used to model signals recorded from complex systems and complex physical phenomena like turbulence, so we are convinced that this new measure can successfully be applied in time series analysis. In particular, we present an example of such application to highly complex empirical data from financial markets. The present formulation can straightforwardly be extended to multivariate data in terms of the $q$-dependent counterpart of the correlation matrices and then to the network representation.
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中文摘要：
最近提出了去趋势互相关系数$\\rho_{\\rm DCCA}$来量化二元非平稳时间序列中不同时间尺度上的互相关强度。它基于去趋势互相关分析和去趋势波动分析（分别为DCCA和DFA），在波动分析中可被视为皮尔逊系数的类似物。系数$\\rho_{\\rm DCCA}$在许多实际情况下运行良好，但通过构造，其适用性仅限于检测两个信号是否通常互相关，而不可能获得有关导致这些互相关的波动幅度的信息。为了引入一些相关的灵活性，这里我们提出了$\\rho_{\\rm DCCA}$的扩展，它分别利用了DFA和DCCA的多重分形版本：MFDFA和MFCCA。由此产生的新系数$\\rho_q$不仅能够量化相关性的强度，而且还可以识别研究中两个信号中相关的去趋势波动幅度范围。通过将系数$\\rho_q$应用于表示长记忆过程的随机时间序列，我们展示了它在实际情况下是如何工作的：自回归和乘法过程。这类过程通常用于模拟复杂系统和复杂物理现象（如湍流）记录的信号，因此我们相信这种新方法可以成功地应用于时间序列分析。特别是，我们给出了一个应用于金融市场高度复杂的经验数据的例子。目前的公式可以直接扩展到多元数据，即相关矩阵的$q$依赖对应项，然后扩展到网络表示。
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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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