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.
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September 2015
Research Article|
April 13 2015
Nonlinear time-series analysis revisited
Elizabeth Bradley;
Elizabeth Bradley
a)
1Department of Computer Science,
University of Colorado
, Boulder, Colorado 80309-0430, USA
and Santa Fe Institute
, Santa Fe, New Mexico 87501, USA
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Holger Kantz
Holger Kantz
b)
2
Max Planck Institute for the Physics of Complex Systems
, Noethnitzer Str. 38 D, 01187 Dresden, Germany
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a)
Electronic mail: lizb@cs.colorado.edu
b)
Electronic mail: kantz@pks.mpg.de
Chaos 25, 097610 (2015)
Article history
Received:
January 27 2015
Accepted:
March 26 2015
Citation
Elizabeth Bradley, Holger Kantz; Nonlinear time-series analysis revisited. Chaos 1 September 2015; 25 (9): 097610. https://doi.org/10.1063/1.4917289
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