Departamento de Física, Universidade Estadual de Maringá, Maringá, PR 87020-900, Brazil.
Centro de Investigaciones Ópticas (CONICET La Plata - CIC), C.C. 3, 1897 Gonnet, Argentina.
Phys Rev E. 2017 Jun;95(6-1):062106. doi: 10.1103/PhysRevE.95.062106. Epub 2017 Jun 5.
The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only capture a single aspect of the system dynamics. Here, we propose a family of complexity measures for time series based on a generalization of the complexity-entropy causality plane. By replacing the Shannon entropy by a monoparametric entropy (Tsallis q entropy) and after considering the proper generalization of the statistical complexity (q complexity), we build up a parametric curve (the q-complexity-entropy curve) that is used for characterizing and classifying time series. Based on simple exact results and numerical simulations of stochastic processes, we show that these curves can distinguish among different long-range, short-range, and oscillating correlated behaviors. Also, we verify that simulated chaotic and stochastic time series can be distinguished based on whether these curves are open or closed. We further test this technique in experimental scenarios related to chaotic laser intensity, stock price, sunspot, and geomagnetic dynamics, confirming its usefulness. Finally, we prove that these curves enhance the automatic classification of time series with long-range correlations and interbeat intervals of healthy subjects and patients with heart disease.
在处理复杂系统时，寻找时间序列中的模式是一项非常常见的任务。这通常通过使用复杂度度量来完成，例如熵和分形维数。然而，这些度量通常只捕捉系统动态的单个方面。在这里，我们基于复杂度-熵因果关系平面的推广，提出了一类基于时间序列的复杂度度量。通过用单参数熵（Tsallis q 熵）替换香农熵，并考虑统计复杂度（q 复杂度）的适当推广，我们构建了一条参数曲线（q-复杂度-熵曲线），用于描述和分类时间序列。基于简单的精确结果和随机过程的数值模拟，我们表明这些曲线可以区分不同的长程、短程和振荡相关行为。此外，我们验证了模拟的混沌和随机时间序列可以根据这些曲线是开放的还是封闭的来区分。我们进一步在与混沌激光强度、股票价格、太阳黑子和地磁动力学相关的实验场景中测试了该技术，证实了它的有效性。最后，我们证明这些曲线可以增强具有长程相关性和健康受试者和心脏病患者的心跳间隔的时间序列的自动分类。
