Nonlinear time-series analysis revisited
Nonlinear time-series analysis revisited
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DOI：
10.1063/1.4917289
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发表时间：
2015-09-01
期刊：
影响因子：
2.9
通讯作者：
Kantz, Holger
中科院分区：
文献类型：
--
作者：
Bradley, Elizabeth;Kantz, Holger
1980年和1981年，两篇开创性的论文奠定了后来被称为非线性时间序列分析的基础：通过动力系统理论对观测数据--通常是单变量--进行分析。基于状态空间重构的概念，这套方法允许我们计算诸如Lyapunov指数和分维等特征量，预测时间序列的未来过程，甚至在某些情况下重构运动方程。然而，在实践中，有许多问题限制了这种方法的能力：例如，信号是否准确和彻底地对动态进行采样，以及它是否包含噪声。此外，我们用来实例化这些思想的数值算法并不完美；它们涉及近似、尺度参数和有限精度算术等。即便如此，非线性时间序列分析在从轮盘赌轮盘、激光到人体心脏等各种系统的数千个真实和合成数据集上得到了极大的优势。即使在数据不满足确保完全拓扑共轭的数学或算法要求的情况下，非线性时间序列分析的结果也可以帮助理解、表征和预测动态系统。(C)2015 AIP出版有限责任公司。
In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data-typically univariate-via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems. (c) 2015 AIP Publishing LLC.