Kathpalia Aditi, Nagaraj Nithin
Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Czech Academy of Sciences, Pod Vodárenskou věží 271/2, 182 07 Prague, Czech Republic.
Consciousness Studies Programme, National Institute of Advanced Studies (NIAS), Indian Institute of Science Campus, Bengaluru 560012, India.
Entropy (Basel). 2021 Mar 10;23(3):327. doi: 10.3390/e23030327.
Detection of the temporal reversibility of a given process is an interesting time series analysis scheme that enables the useful characterisation of processes and offers an insight into the underlying processes generating the time series. Reversibility detection measures have been widely employed in the study of ecological, epidemiological and physiological time series. Further, the time reversal of given data provides a promising tool for analysis of causality measures as well as studying the causal properties of processes. In this work, the recently proposed measure (by the authors) is shown to be free of the assumption that the "cause precedes the effect", making it a promising tool for causal analysis of reversible processes. CCC is a data-driven interventional measure of causality (second rung on the ) that is based on , a well-established robust method to characterize the complexity of time series for analysis and classification. For the detection of the temporal reversibility of processes, we propose a novel measure called the . This asymmetry measure compares the probability of the occurrence of patterns at different scales between the forward-time and time-reversed process using ETC. We test the performance of the measure on a number of simulated processes and demonstrate its effectiveness in determining the asymmetry of real-world time series of sunspot numbers, digits of the transcedental number π and heart interbeat interval variability.
检测给定过程的时间可逆性是一种有趣的时间序列分析方案，它能够对过程进行有效的特征描述，并深入了解生成时间序列的潜在过程。可逆性检测方法已广泛应用于生态、流行病学和生理时间序列的研究中。此外，给定数据的时间反转提供了一个有前景的工具，用于因果关系度量分析以及研究过程的因果特性。在这项工作中，作者最近提出的度量方法被证明不受“原因先于结果”这一假设的限制，使其成为可逆过程因果分析的一个有前景的工具。CCC是一种基于数据驱动的因果关系干预度量（位于因果关系阶梯的第二级），它基于一种成熟的稳健方法来表征时间序列的复杂性，用于分析和分类。为了检测过程的时间可逆性，我们提出了一种名为 的新度量方法。这种不对称性度量使用ETC比较正向时间过程和时间反转过程在不同尺度上模式出现的概率。我们在多个模拟过程上测试了该度量方法的性能，并证明了它在确定太阳黑子数、超越数π的数字以及心脏心跳间期变异性等实际时间序列的不对称性方面的有效性。
