Nonlinear time-series analysis revisited

Abstract

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.

References in corpus (13)

• Recurrence Plots for the Analysis of Complex Systems
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• Surrogate time series
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• Don't bleach chaotic data
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• Series2Graph: Graph-based Subsequence Anomaly Detection for Time Series
• ordpy: A Python package for data analysis with permutation entropy and ordinal network methods
• Using reservoir computers to distinguish chaotic signals
• Nonlinear stochastic modeling with Langevin regression
• Trends in recurrence analysis of dynamical systems
• On Causality in Dynamical Systems
• Training Echo State Networks with Regularization through Dimensionality Reduction
• Exploring the Topology of Dynamical Reconstructions
• Estimating fractal dimensions: a comparative review and open source implementations
• Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time series analysis
• Anomaly Detection in Paleoclimate Records using Permutation Entropy
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• Prediction in Projection
• Mapping images into ordinal networks
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• Topological time-series analysis with delay-variant embedding
• Right-side-stretched multifractal spectra indicate small-worldness in networks
• Deep learning delay coordinate dynamics for chaotic attractors from partial observable data
• Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems
• Predicting Spatio-Temporal Time Series Using Dimension Reduced Local States
• Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps
• Revisiting Evidence of Chaos in X-ray Light Curves: The Case of GRS 1915+105
• Exploiting the impact of ordering patterns in the Fisher-Shannon complexity plan
• Computational Topology Techniques for Characterizing Time-Series Data
• Averaged Recurrence Quantification Analysis -- Method omitting the recurrence threshold choice
• Using Curvature to Select the Time Lag for Delay Reconstruction
• Sampling rate-corrected analysis of irregularly sampled time series
• Deterministic Aspect of the $\gamma$-ray Variability in Blazars
• Measuring chaos in the Lorenz and Rössler models: Fidelity tests for reservoir computing
• Incomplete Phase-Space Method to Reveal Time Delay From Scalar Time-series
• Using scaling-region distributions to select embedding parameters
• Towards automated extraction and characterization of scaling regions in dynamical systems
• Non-parametric power-law surrogates
• Bimodality and Scaling in Recurrence Networks from ECG data
• Analysis of chaotic dynamical systems with autoencoders
• Topological EEG Nonlinear Dynamics Analysis for Emotion Recognition
• Physical realization of complex dynamical pattern formation in magnetic active feedback rings
• Recurrence analysis of meteorological data from climate zones in India
• The partial visibility curve of the Feigenbaum cascade to chaos
• Multivariate time series approximation by multiple trajectories of a dynamical system. Applications to Internet traffic and COVID-19 data
• Approximate Bayesian Computation with Path Signatures
• Phase Walk Analysis of Leptokurtic Time Series
• Prediction in Projection: A new paradigm in delay-coordinate reconstruction
• Reconstruction of Delay Differential Equation via Learning Parameterized Dictionary
• ComplexityMeasures.jl: scalable software to unify and accelerate entropy and complexity timeseries analysis
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• Dynamical systems theory for causal inference with application to synthetic control methods
• Evolutionary Games, Complex Networks and Nonlinear Analysis for Epileptic Seizures Forecasting
• Nonchaotic Models and Predictability of the Users' Volume Dynamics on Internet Platforms
• Computing with bricks and mortar: Classification of waveforms with a doped concrete blocks