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Testing dynamic correlations and nonlinearity in bivariate time series through information measures and surrogate

Helder Pinto1,2, Ivan Lazic3, Yuri Antonacci4

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This study introduces novel surrogate data methods to analyze complex time series. Paced breathing at low rates enhances predictability in heart period and respiratory flow, while reducing their nonlinear coupling.

Keywords:
complex systemscouplinginformation storageinformation theorymutual information ratesurrogate analysis

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Area of Science:

  • Dynamical systems analysis
  • Nonlinear time series analysis
  • Physiological signal processing

Background:

  • Time series data analysis is crucial for understanding system dynamics.
  • Surrogate data testing provides robust statistical validation for observed phenomena.
  • Distinguishing deterministic from stochastic systems requires advanced analytical tools.

Purpose of the Study:

  • To develop and validate novel surrogate methods for assessing statistical properties in random processes.
  • To evaluate the presence of autodependencies, nonlinear dynamics, coupling, and nonlinearities in univariate and bivariate processes.
  • To apply these methods to physiological time series for insights into cardiorespiratory interactions.

Main Methods:

  • Formulating null hypotheses and testing them with surrogate data.
  • Utilizing Information Storage as a discriminating statistic for univariate processes.
  • Employing Mutual Information Rate for detecting coupling and nonlinearities in bivariate processes.
  • Testing methods via simulations and application to human physiological data (RR intervals and RESP).

Main Results:

  • Simulations confirmed the effectiveness of proposed methods in identifying dynamical features of stochastic systems.
  • Paced breathing at low rates increased the predictability of individual RR interval and RESP dynamics.
  • Paced breathing at low rates reduced the nonlinearity in the coupled dynamics of RR and RESP.

Conclusions:

  • The developed surrogate methods are effective for analyzing complex time series data.
  • Paced breathing significantly alters the dynamics and coupling of cardiorespiratory signals.
  • These findings have implications for understanding physiological regulation and developing advanced analytical techniques.