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Related Experiment Videos

Recurrence time analysis, long-term correlations, and extreme events.

Eduardo G Altmann1, Holger Kantz

  • 1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany. edugalt@pks.mpg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
Summary

Statistical recurrence time analysis and Poincaré recurrence time methods are compared. Findings reveal that time series correlations impact recurrence statistics, showing a lack of invariance under observable changes.

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Area of Science:

  • Applies to diverse scientific fields analyzing extreme events and nonlinear dynamical systems.

Background:

  • Recurrence times between extreme events are crucial for statistical analysis.
  • Poincaré recurrence time is a key metric for characterizing nonlinear dynamical systems.

Purpose of the Study:

  • To compare statistical recurrence time analysis with Poincaré recurrence time methods.
  • To investigate the impact of probability density, observation intervals, and temporal correlations on recurrence analysis in time series.

Main Methods:

  • Comparative analysis of statistical recurrence time methods and Poincaré recurrence time.
  • Examination of time series properties including probability density, observation intervals, and temporal correlations.
  • Verification of the stretched exponential distribution for long-term correlated processes.

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Main Results:

  • Recurrence time statistics are dependent on probability density, observation intervals, and temporal correlations.
  • The stretched exponential distribution is valid for linear long-term correlated processes, defined by exponent gamma.
  • Transformations altering time series correlations can change recurrence statistics, indicating a lack of invariance.

Conclusions:

  • The choice of observable significantly affects recurrence time statistics, highlighting limitations in invariance.
  • Understanding these dependencies is critical for accurate recurrence analysis in various scientific time series.