Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.

中文翻译：

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使用多尺度序数量词的时延识别

由于物理量的传播速度有限，时滞相互作用自然会出现在众多现实世界的系统中。通常，外部观察者不知道相互作用的时间尺度，需要从观察数据的时间序列中推断出来。在这项工作中，我们探索了几个基于序数的量词的属性，用于从时间序列中识别时间延迟。为此，我们生成了随机和确定性时间延迟模型的人工时间序列。我们发现生成模型中非线性的存在会对序数模式的分布产生影响，从而影响量词的延迟识别质量。这里，我们提出了一种新的基于序数的量词，它对生成模型中的非线性特别敏感，并将其与先前定义的量词进行比较。我们通过对人工生成数据的分析得出结论，正确识别时间延迟的存在及其从时间序列中的精确值得益于基于序数的量词和标准自相关函数的互补使用。我们通过来自北大西洋涛动天气现象的真实世界数据的实际示例进一步验证了这些工具。我们通过对人工生成数据的分析得出结论，正确识别时间延迟的存在及其从时间序列中的精确值得益于基于序数的量词和标准自相关函数的互补使用。我们通过来自北大西洋涛动天气现象的真实世界数据的实际示例进一步验证了这些工具。我们通过对人工生成数据的分析得出结论，正确识别时间延迟的存在及其从时间序列中的精确值得益于基于序数的量词和标准自相关函数的互补使用。我们通过来自北大西洋涛动天气现象的真实世界数据的实际示例进一步验证了这些工具。