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Multiwavelet scale multidimensional recurrence quantification analysis.

Qian He1, Jingjing Huang1

  • 1School of Science, Beijing Information Science and Technology University, Beijing 100192, People's Republic of China.

Chaos (Woodbury, N.Y.)
|December 31, 2020
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Summary
This summary is machine-generated.

A new multiwavelet scale multidimensional recurrence quantification analysis (MWMRQA) method quantifies time series recurrence properties across scales. This approach reveals dynamic variations in systems like the Lorenz model and Chinese stock market.

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Area of Science:

  • Complex Systems Science
  • Time Series Analysis
  • Nonlinear Dynamics

Background:

  • Traditional recurrence quantification analysis (RQA) methods may not fully capture multi-scale dynamics in complex systems.
  • Wavelet decomposition is effective for analyzing signals at different frequency scales.
  • Integrating these approaches can offer deeper insights into time series behavior.

Purpose of the Study:

  • To introduce a novel method, multiwavelet scale multidimensional recurrence quantification analysis (MWMRQA), for analyzing multidimensional time series.
  • To quantify the recurrence properties of time series across various wavelet scales.
  • To demonstrate the method's applicability and reveal scale-dependent dynamics in established systems.

Main Methods:

  • The proposed MWMRQA method combines multidimensional recurrence quantification analysis (MDRQA) with wavelet packet decomposition.
  • This integration allows for the examination of recurrence patterns at different wavelet scales within a single multidimensional time series.
  • The method was applied to the chaotic Lorenz system and the Chinese stock market data.

Main Results:

  • The study successfully demonstrates the feasibility of the MWMRQA method.
  • Application to the Lorenz system revealed scale-dependent dynamic variations.
  • Analysis of the Chinese stock market also showed dynamic changes across different wavelet scales, highlighting market complexity.

Conclusions:

  • The MWMRQA method provides a robust framework for quantifying multi-scale recurrence properties in multidimensional time series.
  • It offers a new perspective for analyzing complex systems, including financial markets and physical models.
  • This technique has potential applications in various scientific disciplines requiring scale-specific time series analysis.