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Time-Reversibility, Causality and Compression-Complexity.

Aditi Kathpalia1,2, Nithin Nagaraj2

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Summary
This summary is machine-generated.

We introduce a new method to detect temporal reversibility in time series data. This approach, based on compression complexity, offers insights into causal relationships and process dynamics.

Keywords:
compression-complexitycompressive potentialeffort-to-compressheart period variability asymmetryinterventional causalitysunspot numberstemporal asymmetrytime-irreversibilitytime-reversibility

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Area of Science:

  • Complex Systems Analysis
  • Time Series Analysis
  • Causality Studies

Background:

  • Temporal reversibility detection is crucial for characterizing processes and understanding underlying dynamics.
  • Existing measures are widely used in ecological, epidemiological, and physiological time series.
  • Time reversal analysis aids in studying causality and causal properties of processes.

Purpose of the Study:

  • To introduce a novel measure for detecting temporal reversibility in processes.
  • To demonstrate the utility of the Compression-Complexity Causality (CCC) measure for analyzing reversible processes.
  • To present the Compressive Potential based Asymmetry Measure for quantifying temporal asymmetry.

Main Methods:

  • Utilized the Compression-Complexity Causality (CCC) measure, a data-driven interventional causality measure.
  • Employed Effort-to-Compress (ETC) to characterize time series complexity and identify pattern probabilities.
  • Developed the Compressive Potential based Asymmetry Measure to compare forward and time-reversed processes.

Main Results:

  • The proposed Compressive Potential based Asymmetry Measure effectively detects temporal reversibility.
  • Demonstrated the measure's performance on simulated and real-world time series data.
  • Confirmed the measure's ability to determine asymmetry in sunspot numbers, digits of pi, and heart rate variability.

Conclusions:

  • The novel asymmetry measure provides a robust tool for analyzing temporal reversibility.
  • The CCC measure is suitable for causal analysis of reversible processes, independent of the 'cause precedes effect' assumption.
  • This work advances the understanding of complex systems through advanced time series analysis.