Entropic and algebraic transcript-based tools in time series analysis

Area of Science:

• Dynamical Systems and Time Series Analysis
• Information Theory
• Group Theory

Background:

• Coupled time series analysis is crucial for understanding complex systems.
• Algebraic representations, such as ordinal patterns (permutations), offer a structured way to analyze time series.
• Existing transcript-based tools have limitations in capturing complex couplings.

Purpose of the Study:

• To outline and compare existing entropic and algebraic transcript-based tools for coupled time series analysis.
• To introduce a novel similarity distance for evaluating coupled time series.
• To assess the performance of these tools in detecting generalized synchronization.

Main Methods:

• Utilizing algebraic representations (group-valued time series) and their inherent group structure.
• Applying transcript-based analysis, including entropic measures (entropy, divergence, statistical complexity, mutual information) and algebraic measures (order classes, Cayley distance, Kendall distance).
• Developing and evaluating a new similarity distance based on the mean Kendall distance.

Main Results:

• Existing entropic and algebraic tools were reviewed and compared.
• The newly proposed similarity distance was introduced as a mean Kendall distance.
• The similarity distance demonstrated superior performance in detecting generalized synchronization compared to other tested tools.

Conclusions:

• Transcript-based methods provide valuable insights into coupled time series.
• The novel similarity distance is a promising tool for analyzing coupled systems.
• This approach enhances the detection of phenomena like generalized synchronization in complex systems.