通过信息度量和代用数据分析测试双变量时间序列中的动态相关性和非线性

Hélder Pinto, Ivan Lazic, Y. Antonacci, R. Pernice, Danlei Gu, Chiara Barà, L. Faes, Ana Paula Rocha
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引用次数: 0

摘要

描述物理系统特性演变的时间序列数据越来越多,这促使人们开发出各种方法,重点是深入了解系统随时间变化的行为,分辨它是源于确定性动态系统还是随机动态系统。代用数据测试通过促进稳健的统计评估,在这一过程中发挥着至关重要的作用。这可以确保观察到的结果并非偶然发生,而是真正反映了底层系统的固有特征。最初的过程包括提出一个零假设,并在不存在基本分布假设的情况下使用代用数据进行检验。然后对原始数据和每个代用数据集计算判别统计量。原始数据和代用数据集合之间的显著偏差值会导致拒绝零假设。在这项工作中,我们介绍了各种旨在评估随机过程中特定统计属性的代用方法。具体来说,我们介绍了评估单个过程中是否存在自依赖性和非线性动态的方法,并将信息存储作为一种判别统计量。此外,我们还介绍了检测双变量过程中耦合性和非线性的方法,并为此使用了互信息率。介绍的代用方法首先通过涉及单变量和双变量过程的模拟进行测试,这些过程既有线性动态过程,也有非线性动态过程。然后,将其应用于在自主呼吸和起搏呼吸过程中测量的心脏周期(RR 间隔)和呼吸流量(RESP)变异性的生理时间序列。模拟结果表明,所提出的方法能有效识别随机系统的基本动态特征。实际数据应用表明,低呼吸频率下的节律呼吸提高了 RR 和 RESP 各自动态的可预测性,并抑制了它们耦合动态的非线性。
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Testing dynamic correlations and nonlinearity in bivariate time series through information measures and surrogate data analysis
The increasing availability of time series data depicting the evolution of physical system properties has prompted the development of methods focused on extracting insights into the system behavior over time, discerning whether it stems from deterministic or stochastic dynamical systems. Surrogate data testing plays a crucial role in this process by facilitating robust statistical assessments. This ensures that the observed results are not mere occurrences by chance, but genuinely reflect the inherent characteristics of the underlying system. The initial process involves formulating a null hypothesis, which is tested using surrogate data in cases where assumptions about the underlying distributions are absent. A discriminating statistic is then computed for both the original data and each surrogate data set. Significantly deviating values between the original data and the surrogate data ensemble lead to the rejection of the null hypothesis. In this work, we present various surrogate methods designed to assess specific statistical properties in random processes. Specifically, we introduce methods for evaluating the presence of autodependencies and nonlinear dynamics within individual processes, using Information Storage as a discriminating statistic. Additionally, methods are introduced for detecting coupling and nonlinearities in bivariate processes, employing the Mutual Information Rate for this purpose. The surrogate methods introduced are first tested through simulations involving univariate and bivariate processes exhibiting both linear and nonlinear dynamics. Then, they are applied to physiological time series of Heart Period (RR intervals) and respiratory flow (RESP) variability measured during spontaneous and paced breathing. Simulations demonstrated that the proposed methods effectively identify essential dynamical features of stochastic systems. The real data application showed that paced breathing, at low breathing rate, increases the predictability of the individual dynamics of RR and RESP and dampens nonlinearity in their coupled dynamics.
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