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Characterizing time series via complexity-entropy curves.

Haroldo V Ribeiro1, Max Jauregui1, Luciano Zunino2,3

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This study introduces a new method for analyzing time series complexity using generalized Tsallis q entropy and q complexity. These q-complexity-entropy curves effectively classify diverse time series patterns, including chaotic and stochastic behaviors.

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Area of Science:

  • Complex Systems Analysis
  • Nonlinear Dynamics
  • Information Theory

Background:

  • Time series analysis is crucial for understanding complex systems.
  • Existing complexity measures like Shannon entropy and fractal dimensions capture only limited aspects of system dynamics.
  • A need exists for more comprehensive complexity measures.

Purpose of the Study:

  • To propose a generalized complexity-entropy causality plane using Tsallis q entropy and q complexity.
  • To develop a parametric curve (q-complexity-entropy curve) for time series characterization and classification.
  • To demonstrate the effectiveness of this new method in distinguishing various time series behaviors.

Main Methods:

  • Generalization of the complexity-entropy causality plane by incorporating Tsallis q entropy and q complexity.
  • Construction and analysis of the parametric q-complexity-entropy curve.
  • Numerical simulations of stochastic and chaotic processes.
  • Application to experimental time series data (laser intensity, stock prices, sunspots, geomagnetic data).

Main Results:

  • The q-complexity-entropy curves successfully distinguish between long-range, short-range, and oscillating correlated behaviors.
  • Chaotic and stochastic time series can be differentiated by the open or closed nature of these curves.
  • The method demonstrated utility in analyzing real-world experimental data.
  • Enhanced automatic classification of time series with long-range correlations and interbeat intervals was achieved.

Conclusions:

  • The proposed q-complexity-entropy curves offer a powerful and versatile tool for time series analysis and classification.
  • This generalized approach overcomes limitations of traditional complexity measures.
  • The technique shows significant potential for applications in diverse scientific and medical fields.