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A Brief Introduction to Nonlinear Time Series Analysis and Recurrence Plots

Potsdam Institute for Climate Impact Research, Transdisciplinary Concepts & Methods, 14412 Potsdam, Germany
Vibration 2019, 2(4), 332-368; https://doi.org/10.3390/vibration2040021
Received: 21 February 2019 / Revised: 29 November 2019 / Accepted: 2 December 2019 / Published: 8 December 2019
(This article belongs to the Special Issue Irregular Engineering Oscillations and Signal Processing)
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. View Full-Text
Keywords: time series analysis; nonlinear systems; recurrence plots; surrogate data; hypothesis testing; complex systems; recurrence networks time series analysis; nonlinear systems; recurrence plots; surrogate data; hypothesis testing; complex systems; recurrence networks
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Goswami, B. A Brief Introduction to Nonlinear Time Series Analysis and Recurrence Plots. Vibration 2019, 2, 332-368.

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