Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces
Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces
复制标题
常见外力影响下两个非平稳时间序列的去趋势偏互相关分析
DOI：
10.1103/physreve.91.062816
复制
发表时间：
2015-06-26
影响因子：
2.4
通讯作者：
Stanley, H. Eugene
中科院分区：
文献类型：
--
作者：
Qian, Xi-Yuan;Liu, Ya-Min;Stanley, H. Eugene
当共同因素强烈影响在复杂的自然或社会系统中记录的两个幂律交叉相关时间序列时，使用不考虑这些共同因素的去趋势相互关联分析（DCCA）将使结果产生偏差。在去除其他时间序列作为共同力的影响后，我们使用去趋势偏互相关分析（DPXA）来揭示在存在非平稳性的情况下，两个同时记录的时间序列之间的内在幂律相互关系。DPXA方法是考虑了偏相关分析的去趋势互相关分析的推广。我们用带有分数布朗运动的二元分数布朗运动来证明该方法。我们发现DPXA能够恢复解析交叉Hurst指数，因此多尺度DPXA系数是传统相互相关系数的可行替代方案。通过分析受污染的二元分数布朗运动，我们证明了DPXA系数优于DCCA系数。我们计算DPXA系数，并在考虑美元指数影响的情况下，利用DPXA系数提取原油与黄金期货的内在相互关系。为了推广DPXA方法，研究多重分形时间序列，提出了多重分形DPXA （MF-DPXA）方法。分析了被强白噪声掩盖的多重分形二项测度，发现MF-DPXA方法量化了多重分形的隐藏性质，而多重分形DCCA方法则失败。
When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using detrended cross-correlation analysis (DCCA) without considering these common factors will bias the results. We use detrended partial cross-correlation analysis (DPXA) to uncover the intrinsic power-law cross correlations between two simultaneously recorded time series in the presence of nonstationarity after removing the effects of other time series acting as common forces. The DPXA method is a generalization of the detrended cross-correlation analysis that takes into account partial correlation analysis. We demonstrate the method by using bivariate fractional Brownian motions contaminated with a fractional Brownian motion. We find that the DPXA is able to recover the analytical cross Hurst indices, and thus the multiscale DPXA coefficients are a viable alternative to the conventional cross-correlation coefficient. We demonstrate the advantage of the DPXA coefficients over the DCCA coefficients by analyzing contaminated bivariate fractional Brownian motions. We calculate the DPXA coefficients and use them to extract the intrinsic cross correlation between crude oil and gold futures by taking into consideration the impact of the U.S. dollar index. We develop the multifractal DPXA (MF-DPXA) method in order to generalize the DPXA method and investigate multifractal time series. We analyze multifractal binomial measures masked with strong white noises and find that the MF-DPXA method quantifies the hidden multifractal nature while the multifractal DCCA method fails.