Zanin Massimiliano, Rodríguez-González Alejandro, Menasalvas Ruiz Ernestina, Papo David
Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, 28040 Madrid, Spain.
Department of Computer Science, Faculty of Science and Technology, Universidade Nova de Lisboa, 2829-516 Lisboa, Portugal.
Entropy (Basel). 2018 Sep 3;20(9):665. doi: 10.3390/e20090665.
Time irreversibility, i.e., the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here, we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation.
时间不可逆性，即系统的统计特性在时间反演下缺乏不变性，是所有非平衡态运行系统的一个基本属性。时间反演对称性与重要的统计和物理特性相关联，并且与生成时间序列的系统的可预测性有关。在过去的十五年里，已经提出了各种量化时间序列中时间不可逆性的方法，但这些方法在计算上可能成本高昂。在此，我们提出一种基于排列熵的新方法，该方法本质上无参数、具有时间局部性、能给出直接的统计检验，并且具有快速收敛特性。我们将此方法应用于金融时间序列研究，表明股票和指数呈现出丰富的不可逆动力学。我们通过与最近提出的基于可见性图的方法对比来说明我们方法在方法论上的优势，并讨论我们的结果对金融数据分析和解释的意义。
