Abstract
Nonlinear time series analysis gained prominence from the late 1980s on, primarily because of its ability to characterize, analyze, and predict nontrivial features in data sets that stem from a wide range of fields such as finance, music, human physiology, cognitive science, astrophysics, climate, and engineering. More recently, recurrence plots, initially proposed as a visual tool for the analysis of complex systems, have proven to be a powerful framework to quantify and reveal nontrivial dynamical features in time series data. This tutorial review provides a brief introduction to the fundamentals of nonlinear time series analysis, before discussing in greater detail a few (out of the many existing) approaches of recurrence plot-based analysis of time series. In particular, it focusses on recurrence plot-based measures which characterize dynamical features such as determinism, synchronization, and regime changes. The concept of surrogate-based hypothesis testing, which is crucial to drawing any inference from data analyses, is also discussed. Finally, the presented recurrence plot approaches are applied to two climatic indices related to the equatorial and North Pacific regions, and their dynamical behavior and their interrelations are investigated.
Highlights
A seminal event in the history of time series analysis was the discovery of nonlinear behavior, such as deterministic chaos and self-similarity, in the 1960s
The approaches based on recurrence plots are collectively referred to as ‘recurrence quantification analysis’ (RQA), and they form the core of recurrence plot-based techniques
Stender et al [76] used RQA to demonstrate that friction-induced vibrations (FIV) are multiscale in nature, that squealing is consistent with low dimensional attractors, and that the higher vibration levels correspond to higher determinism and periodicity of the dynamics
Summary
A seminal event in the history of time series analysis was the discovery of nonlinear behavior, such as deterministic chaos and self-similarity, in the 1960s. The paradigm of nonlinear dynamical systems provided an additional and fundamentally different route by which to approach real-world complex systems It was not until the early ’80s, that the theoretical developments of nonlinear dynamical systems began to give rise to new time series analysis techniques. The recurrence plot was a simple, estimable, visual aid to characterize the dynamics of a system It was based solely on the measured time series and was designed to complement new approaches of the time that estimated various nonlinear dynamical characteristics such as the Lyapunov exponent [37], information dimension [38], and correlation dimension [10]. Walker and Small [58] use recurrence plots in combination with the previously established ‘quadrant scan’ technique [59] to identify tipping points of dynamical systems and demonstrate their approach with real-world examples such as petrophysical data from a geological well in Australia, electrocardiogram (ECG) data recording cardiac arythmia, and EEG data of a person doing a multiplication task
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