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Assessing time irreversibility in data is challenging due to its varied causes. This study reviews numerical methods for time series analysis and provides an open-source library, highlighting that no single test fits all applications.

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Area of Science:

  • Complex Systems Science
  • Data Analysis
  • Time Series Analysis

Background:

  • Time irreversibility, the lack of invariance under time reversal, is increasingly recognized in diverse systems.
  • Irreversible dynamics are linked to pathologies (e.g., brain, heart, gait) and market inefficiencies.
  • Assessing time series irreversibility is complex due to multiple causes and data manifestations.

Purpose of the Study:

  • To review and compare numerical methods for testing time series irreversibility.
  • To analyze the hypotheses, limitations, and performance of existing algorithms.
  • To provide an open-source software library for irreversibility tests.

Main Methods:

  • Comprehensive literature review of time series irreversibility detection algorithms.
  • Comparative analysis of algorithmic performance, computational, and practical limitations.
  • Development and provision of an open-source software library.

Main Results:

  • Multiple numerical methods exist for assessing time series irreversibility, each with unique strengths and weaknesses.
  • The effectiveness and applicability of tests vary depending on the specific data and research question.
  • No single method universally captures all aspects of time irreversibility.

Conclusions:

  • Time series irreversibility assessment requires careful selection of appropriate methods.
  • Different tests offer complementary, and sometimes conflicting, insights.
  • Further research is needed to develop more robust and versatile irreversibility detection techniques.