Dispersion complexity-entropy curves: An effective method to characterize the structures of nonlinear time series

Area of Science:

• Nonlinear dynamics
• Time series analysis
• Complexity science

Background:

• Complexity-Entropy Curves (CEC) are vital for time series analysis.
• Permutation Complexity-Entropy Curve (PCEC) using Permutation Entropy (PE) overlooks series means and amplitudes, limiting accuracy.
• Dispersion Entropy (DE) offers an alternative approach to entropy calculation.

Purpose of the Study:

• Introduce the Dispersion Complexity-Entropy Curve (DCEC) to improve CEC's ability to analyze nonlinear time series.
• Address the limitations of PCEC by incorporating amplitude and mean information.
• Demonstrate DCEC's effectiveness in distinguishing diverse time series and its practical applications.

Main Methods:

• Developed DCEC by integrating principles from Dispersion Entropy (DE).
• Validated DCEC using simulated data from logistic maps, color noises, and chaotic systems.
• Applied DCEC to real-world datasets, including bearing fault diagnosis and stock market index analysis.

Main Results:

• DCEC effectively distinguished between nonlinear time series with varied characteristics in simulations.
• DCEC-based feature extraction combined with multivariate support vector machines achieved high accuracy in bearing fault diagnosis.
• Analysis of stock indices using DCEC revealed significant insights into financial market complexity and dynamics.

Conclusions:

• DCEC is a powerful and versatile tool for nonlinear time series analysis, overcoming limitations of previous methods.
• The method demonstrates practical utility in engineering diagnostics and financial market analysis.
• DCEC offers a novel perspective for understanding the complex structures within diverse time series data.