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Detecting causality from nonlinear dynamics with short-term time series.

Huanfei Ma1, Kazuyuki Aihara2, Luonan Chen3

  • 11] School of Mathematical Sciences, Soochow University, China [2] Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, The University of Tokyo, Japan.

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Detecting causality in short time series data is now possible using nonlinear dynamics and attractor embedding theory. Our novel Cross Map Smoothness (CMS) method accurately infers causality even with limited data.

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Area of Science:

  • Nonlinear dynamics
  • Time series analysis
  • Causal inference

Background:

  • Quantifying causality from observed time series data is crucial across disciplines.
  • Conventional methods struggle with short time series data.
  • Nonlinear dynamics offers potential for causality detection.

Purpose of the Study:

  • To develop a method for detecting causality using very short time series data.
  • To leverage embedding theory of attractors for nonlinear dynamics.
  • To introduce a computationally effective algorithm for causality inference.

Main Methods:

  • Utilizing embedding theory of attractors for nonlinear dynamics.
  • Measuring the smoothness of a cross map between observed variables.
  • Developing and applying the Cross Map Smoothness (CMS) algorithm.

Main Results:

  • Causality can be detected with very short time series data.
  • The Cross Map Smoothness (CMS) algorithm accurately infers causality.
  • High accuracy achieved even with limited data points.

Conclusions:

  • The proposed method based on Cross Map Smoothness (CMS) effectively detects causality.
  • The method is validated on both mathematical models and real biological data.
  • This approach advances causality quantification in short time series analysis.