Characterizing the relationship between time series is an important issue in many fields, in particular, in many cases there is a nonlinear correlation between series. This paper provides a new method to study the relationship between time series using the perspective of complex networks. This method converts a time series into a distance matrix and constructs a sequence of nearest neighbor networks, so that the nonlinear relationship between time series is expressed as similarity between networks. In addition, based on the surrogate series, we applied [Formula: see text]-score to characterize the level of significance and analyzed some benchmark models. We not only use the artificial dataset and the real dataset to verify the effectiveness of the proposed method, but also analyze its robustness, which provides an alternative method for detecting nonlinear relationships.

中文翻译：

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基于复杂网络相似度的时间序列非线性相关分析

表征时间序列之间的关系是许多领域的一个重要问题，特别是在许多情况下，序列之间存在非线性相关性。本文提供了一种利用复杂网络的视角研究时间序列之间关系的新方法。该方法将时间序列转换为距离矩阵，构造最近邻网络的序列，从而将时间序列之间的非线性关系表示为网络之间的相似性。此外，基于代理序列，我们应用[公式：见正文]-score来表征显着性水平，并分析了一些基准模型。我们不仅使用人工数据集和真实数据集来验证所提方法的有效性，还分析了其鲁棒性，