Distinguish between Stochastic and Chaotic Signals by a Local Structure-Based Entropy

Area of Science:

• Complex Systems Analysis
• Information Theory
• Time Series Analysis

Background:

• Information entropy is a key complexity measure for time series but struggles with multivariate data due to correlations.
• Existing entropy measures are often ineffective in handling the complexities of multivariate scenarios.

Purpose of the Study:

• To propose a novel complexity measure, Local Structure Entropy (LSE), designed for multivariate time series.
• To evaluate LSE's ability to distinguish between chaotic and stochastic signals.
• To assess LSE's performance in practical applications like financial market analysis and fault detection.

Main Methods:

• Development of Local Structure Entropy (LSE) based on recurrence network concepts.
• Application of LSE to financial market indices (FSTE100, S&P500, SZSI) to assess market sophistication.
• Utilizing LSE with decision tree classifiers for bearing fault detection.

Main Results:

• LSE successfully differentiates multivariate chaotic sequences from stochastic signals.
• The European (FSTE100) and American (S&P500) stock markets exhibit higher LSE values than the Chinese market (SZSI), indicating greater complexity.
• LSE achieved higher recognition accuracy than permutation entropy in bearing fault detection.

Conclusions:

• Local Structure Entropy (LSE) is a robust measure for quantifying complexity in multivariate time series.
• LSE provides insights into the differing complexities of global financial markets.
• LSE demonstrates superior performance in fault diagnosis compared to traditional methods like permutation entropy.