Manshour Pouya
Physics Department, Persian Gulf University, Bushehr 75169, Iran.
Chaos. 2015 Oct;25(10):103105. doi: 10.1063/1.4930839.
In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacency matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.
为了提取随机时间序列中继承的相关信息，最近提出了可见性图算法，通过该算法可以将时间序列映射到复杂网络上。我们证明，可见性算法并非研究时间序列相关方面的合适算法。然后，我们采用水平可见性算法，它更为简单，将分数过程映射到复杂网络上。结果表明，度分布具有抛物线指数形式，且拟合参数与赫斯特指数相关。此外，我们考虑了其他拓扑性质，如邻接矩阵的最大特征值和度相关性，并表明这些拓扑量也可用于预测赫斯特指数，但反持久分数高斯噪声除外。为了解决这个问题，我们考虑了节点度与其在原始时间序列中对应数据值之间的斯皮尔曼相关系数。
