Transfer Information Energy: A Quantitative Indicator of Information Transfer between Time Series

Area of Science:

• Information Theory
• Time Series Analysis
• Computational Neuroscience

Background:

• Transfer Entropy (TE) quantifies information transfer by measuring uncertainty reduction.
• Analyzing complex systems requires robust methods for detecting directional influence between variables.

Purpose of the Study:

• Introduce Transfer Information Energy (TIE) as an alternative to TE.
• Evaluate TIE's efficacy and computational efficiency in real-world applications.
• Compare information transfer dynamics between stock markets and physiological signals.

Main Methods:

• Defined TIE based on Onicescu's Information Energy.
• Applied TIE and TE to stock market index data (Americas, Asia/Pacific, Europe).
• Analyzed bivariate time series of heart rate and breath rate in sleep apnea patients.

Main Results:

• TIE and TE values showed strong correlations across both applications.
• TIE successfully identified information transfer patterns similar to TE.
• TIE demonstrated significant computational speed advantages over TE.

Conclusions:

• TIE is a viable and computationally efficient alternative to TE for analyzing information transfer in time series.
• The findings support TIE's application in financial markets and biomedical signal analysis.
• TIE offers a complementary perspective by measuring certainty increase, similar to TE's uncertainty reduction.