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摘要翻译：
在许多情况下，在复杂系统中同时记录几个信号，这些信号表现出长期的幂律互相关。多重分形离散互相关分析（MF-DCCA）可以用来量化这种互相关，如基于离散波动分析（MF-X-DFA）的MF-DCCA方法。本文提出了一种基于去中心移动平均分析的MF-DCCA算法，称为MF-X-DMA。通过对具有多重分形性质的理论表达式的二元分数布朗运动、二分量自回归分数积分滑动平均过程和二项式测度产生的时间序列对的大量数值实验，比较了MF-X-DMA算法与MF-X-DFA算法的性能。在所有情况下，从MF-X-DMA和MF-X-DFA算法中提取的标度指数$h_{xy}$都非常接近理论值。对于二元分数布朗运动，互相关的标度指数与两个时间序列之间的互相关系数无关，MF-X-DFA和中心MF-X-DMA算法的性能比较好，优于前向和后向MF-X-DMA算法。我们将这些算法应用于两个股票市场指数的收益时间序列及其波动性。对于收益，居中的MF-X-DMA算法给出了$h_{xy}(q)$的最佳估计，因为它的$h_{xy}(2)$最接近于预期的0.5，而MF-X-DFA算法的性能次之。对于挥发物，前向和后向MF-X-DMA算法得到了相似的结果，而中心MF-X-DMA和MF-X-DFA算法不能提取有理多重分形性质。
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英文标题：
《Multifractal detrending moving average cross-correlation analysis》
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作者：
Zhi-Qiang Jiang and Wei-Xing Zhou
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最新提交年份：
2011
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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：Physics and Society 物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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英文摘要：
There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. The multifractal detrended cross-correlation analysis (MF-DCCA) approaches can be used to quantify such cross-correlations, such as the MF-DCCA based on detrended fluctuation analysis (MF-X-DFA) method. We develop in this work a class of MF-DCCA algorithms based on the detrending moving average analysis, called MF-X-DMA. The performances of the MF-X-DMA algorithms are compared with the MF-X-DFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated moving average processes and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents $h_{xy}$ extracted from the MF-X-DMA and MF-X-DFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross-correlation is independent of the cross-correlation coefficient between two time series and the MF-X-DFA and centered MF-X-DMA algorithms have comparative performance, which outperform the forward and backward MF-X-DMA algorithms. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MF-X-DMA algorithm gives the best estimates of $h_{xy}(q)$ since its $h_{xy}(2)$ is closest to 0.5 as expected, and the MF-X-DFA algorithm has the second best performance. For the volatilities, the forward and backward MF-X-DMA algorithms give similar results, while the centered MF-X-DMA and the MF-X-DFA algorithms fails to extract rational multifractal nature.
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PDF链接：
https://arxiv.org/pdf/1103.2577
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