Temporal complexity refers to qualities of a time series that are emergent, erratic, or not easily described by linear processes. Quantifying temporal complexity within a system is key to understanding the time based dynamics of said system. However, many current methods of complexity quantification are not widely used in psychological research because of their technical difficulty, computational intensity, or large number of required data samples. These requirements impede the study of complexity in many areas of psychological science. A method is presented, tangle, which overcomes these difficulties and allows for complexity quantification in relatively short time series, such as those typically obtained from psychological studies. Tangle is a measure of how dissimilar a given process is from simple periodic motion. Tangle relies on the use of a three-dimensional time delay embedding of a one-dimensional time series. This embedding is then iteratively scaled and premultiplied by a modified upshift matrix until a convergence criterion is reached. The efficacy of tangle is shown on five mathematical time series and using emotional stability, anxiety time series data obtained from 65 socially anxious participants over a 5-week period, and positive affect time series derived from a single participant who experienced a major depression episode during measurement. Simulation results show tangle is able to distinguish between different complex temporal systems in time series with as few as 50 samples. Tangle shows promise as a reliable quantification of irregular behavior of a time series. Unlike many other complexity quantification metrics, tangle is technically simple to implement and is able to uncover meaningful information about time series derived from psychological research studies. (PsycInfo Database Record (c) 2021 APA, all rights reserved)

中文翻译：

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Tangle：用于量化短时间序列中复杂性和不稳定行为的指标。

时间复杂性是指时间序列的特性，即涌现的、不稳定的或不容易用线性过程描述的。量化系统内的时间复杂性是理解所述系统基于时间的动态的关键。然而，目前许多复杂性量化方法由于其技术难度、计算强度或所需数据样本量大等原因，并未广泛应用于心理学研究。这些要求阻碍了心理科学许多领域的复杂性研究。提出一个方法，纠结，它克服了这些困难，并允许在相对较短的时间序列中进行复杂性量化，例如通常从心理学研究中获得的那些。缠结是衡量给定过程与简单周期性运动的不同程度的量度。Tangle 依赖于使用一维时间序列的三维时间延迟嵌入。然后，这个嵌入被迭代地缩放并预乘一个修改后的上移矩阵，直到达到收敛标准。纠结的功效显示在五个数学时间序列上，并使用情绪稳定性、在 5 周内从 65 名社交焦虑参与者获得的焦虑时间序列数据，以及从在测量。仿真结果表明，tangle 能够以少至 50 个样本区分时间序列中不同的复杂时间系统。Tangle 有望作为对时间序列不规则行为的可靠量化。与许多其他复杂性量化指标不同，tangle 在技术上实现起来很简单，并且能够从心理学研究中发现有关时间序列的有意义的信息。（PsycInfo 数据库记录 (c) 2021 APA，保留所有权利）tangle 在技术上实现起来很简单，并且能够从心理学研究中发现有关时间序列的有意义的信息。（PsycInfo 数据库记录 (c) 2021 APA，保留所有权利）tangle 在技术上实现起来很简单，并且能够从心理学研究中发现有关时间序列的有意义的信息。（PsycInfo 数据库记录 (c) 2021 APA，保留所有权利）