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Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) - A Method for Quantifying Correlation between

Sebastian Wallot1

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Summary
This summary is machine-generated.

This study introduces Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) to analyze the co-evolution of two multidimensional time-series. A new Diagonal Cross-Recurrence Profile (DCRP) method captures time-lagged coupling, with code provided for practical application.

Keywords:
DCRPMatLabMdCRQAMultidimensional Cross-Recurrence Quantification AnalysisRmultivariate time-series

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Area of Science:

  • Complex systems analysis
  • Time-series analysis
  • Nonlinear dynamics

Background:

  • Traditional Recurrence Quantification Analysis (RQA) quantifies properties of single time-series.
  • Existing methods lack the capacity to analyze the co-evolution and interdependencies between multiple complex time-series.
  • There is a need for advanced analytical tools to understand coupled dynamical systems.

Purpose of the Study:

  • Introduce Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) as an extension of MdRQA.
  • Enable the quantification of the co-evolution of two multidimensional time-series.
  • Develop a method to capture time-lagged coupling between multidimensional time-series.

Main Methods:

  • Extension of Multidimensional Recurrence Quantification Analysis (MdRQA) to bivariate cases, termed MdCRQA.
  • Computation of a Diagonal Cross-Recurrence Profile (DCRP) from MdCRQA output.
  • Description of core concepts and practical application aspects of MdCRQA and DCRP.

Main Results:

  • MdCRQA successfully quantifies the co-evolutionary properties of two multidimensional time-series.
  • The DCRP effectively captures time-lagged coupling between these series.
  • Methodology is supported by provided MatLab and R function implementations.

Conclusions:

  • MdCRQA and DCRP offer novel quantitative tools for analyzing coupled multidimensional time-series.
  • These methods advance the understanding of complex system dynamics and interdependencies.
  • Availability of open-source implementations facilitates broader application and research.