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We developed a new method to determine the direction of interactions in complex systems using time series data. This noise-robust approach accurately quantifies coupling strength and works even with missing data.

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Area of Science:

  • Complex Systems Analysis
  • Time Series Data Science
  • Network Interaction Inference

Background:

  • Inferring causal relationships from time series data in complex systems is a significant challenge.
  • Existing methods often struggle with noise, missing data, and parameter selection.

Purpose of the Study:

  • To introduce a novel, model-free causality measure for quantifying interaction strength in bivariate time series.
  • To develop a robust and accurate method for inferring coupling direction in complex systems.

Main Methods:

  • A state-space-based causality measure derived from cross-distance vectors.
  • The method is model-free, noise-robust, and resilient to artefacts and missing values.
  • Optimal parameter selection procedure proposed to address embedding parameter challenges.

Main Results:

  • The proposed method yields two coupling indices, outperforming established state-space measures in accuracy.
  • Demonstrated robustness to noise and reliability with shorter time series.
  • Successfully detected cardiorespiratory interactions in measured data.

Conclusions:

  • The novel cross-distance vector approach provides a more accurate and reliable way to infer coupling direction in complex systems.
  • The method is practical for real-world applications due to its robustness and efficiency.
  • An efficient implementation is publicly available.