One of the most important aspects of time series is their degree of stochasticity vs. chaoticity. Since the discovery of chaotic maps, many algorithms have been proposed to discriminate between these two alternatives and assess their prevalence in real-world time series. Approaches based on the combination of “permutation patterns” with different metrics provide a more complete picture of a time series’ nature, and are especially useful to tackle pathological chaotic maps. Here, we provide a review of such approaches, their theoretical foundations, and their application to discrete time series and real-world problems. We compare their performance using a set of representative noisy chaotic maps, evaluate their applicability through their respective computational cost, and discuss their limitations.

时间序列最重要的方面之一是它们的随机性与混沌性的程度。自从发现混沌地图以来，已经提出了许多算法来区分这两种替代方案并评估它们在现实世界时间序列中的普遍性。基于“排列模式”与不同度量的组合的方法提供了更完整的时间序列性质图，并且对于处理病理性混沌图特别有用。在这里，我们回顾了这些方法、它们的理论基础以及它们在离散时间序列和现实世界问题中的应用。我们使用一组有代表性的嘈杂混沌图比较它们的性能，通过各自的计算成本评估它们的适用性，并讨论它们的局限性。