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Using forbidden ordinal patterns to detect determinism in irregularly sampled time series.

C W Kulp1, J M Chobot1, B J Niskala1

  • 1The Department of Astronomy and Physics, Lycoming College, Williamsport, Pennsylvania 17701, USA.

Chaos (Woodbury, N.Y.)
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Summary

Forbidden patterns from time series analysis can detect deterministic dynamics even in irregularly sampled data. This method proves effective for low degrees of sampling irregularity, offering insights into complex systems.

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Area of Science:

  • Dynamical Systems and Time Series Analysis
  • Chaos Theory
  • Nonlinear Dynamics

Background:

  • Symbolizing time series into ordinal patterns using the Bandt-Pompe (BP) methodology reveals forbidden patterns.
  • Forbidden patterns, which do not occur in deterministic series, are indicative of deterministic dynamics.

Purpose of the Study:

  • To test the efficacy of forbidden patterns in detecting determinism within irregularly sampled time series.
  • To evaluate the impact of sampling irregularities on the identification of deterministic dynamics.

Main Methods:

  • Analysis of time series data generated from a continuous model system.
  • Investigation of regularly sampled time series to understand the effects of sampling time on forbidden patterns.
  • Examination of two types of irregular sampling: missing data and timing jitter.

Main Results:

  • Forbidden patterns can successfully detect determinism in irregularly sampled time series, particularly at low degrees of irregularity.
  • The study quantifies the effects of sampling time on the number of forbidden patterns observed.
  • The appropriateness of the Bandt-Pompe methodology for irregularly sampled data is discussed.

Conclusions:

  • The presence of forbidden patterns is a viable indicator of deterministic dynamics in irregularly sampled time series.
  • The Bandt-Pompe methodology shows promise for analyzing complex systems with non-uniform sampling intervals.
  • Further research is warranted to explore the limits and applications of this technique in various scientific domains.