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Related Experiment Videos

Regenerating time series from ordinal networks.

Michael McCullough1, Konstantinos Sakellariou1, Thomas Stemler1

  • 1School of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia.

Chaos (Woodbury, N.Y.)
|April 3, 2017
PubMed
Summary

Ordinal networks offer new nonlinear time series analysis methods. These networks, built from chaotic time series, act as stochastic models that capture essential dynamics of the original data.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems analysis
  • Time series modeling

Background:

  • Ordinal networks provide novel nonlinear time series analysis techniques.
  • They serve as stochastic approximations of deterministic time series flows.

Purpose of the Study:

  • To construct ordinal networks from chaotic time series.
  • To regenerate time series via random walks on these networks.
  • To quantify how well network dynamics represent original time series properties.

Main Methods:

  • Ordinal network construction from discrete chaotic time series.
  • Random walk time series regeneration.
  • Recurrence quantification analysis (RQA) on recurrence plots and order recurrence plots.
  • Largest Lyapunov exponent estimation.

Related Experiment Videos

  • Correlation dimension calculation.

    • Main Results:

    • Ordinal networks successfully encode key dynamical properties of original time series.
    • Random walk surrogates retain significant dynamical information.
    • Quantitative analyses confirm the approximation of original dynamics by ordinal network models.

    Conclusions:

    • Ordinal networks derived from univariate time series data function as effective stochastic models.
    • These models approximate crucial dynamical characteristics of the parent systems.
    • The findings support the utility of ordinal networks in nonlinear time series analysis.