Multiscale information storage of linear long-range correlated stochastic processes

Area of Science:

• Complexity Science
• Dynamical Systems Theory
• Information Theory

Background:

• Information storage is crucial for understanding dynamical system complexity in physical and biological processes.
• Existing methods often struggle to capture complexity across multiple timescales, especially with long-range correlations (LRC).
• Multiscale entropy provides a framework for analyzing complexity at different timescales but needs enhancement for LRC.

Purpose of the Study:

• To introduce a parametric approach for computing information storage across multiple timescales in stochastic processes.
• To develop a method that accounts for both short-term dynamics and long-range correlations (LRC).
• To enhance the practical usability of multiscale information storage quantification.

Main Methods:

• Utilized a multiscale entropy framework with linear fractionally integrated autoregressive (ARFI) models.
• Employed state space models to represent low-pass filtered and downsampled ARFI processes.
• Derived analytical expressions for information storage by relating process variance to prediction error variance.

Main Results:

• Demonstrated that LRC substantially alter the complexity of ARFI processes, even at short timescales.
• Showed that reliable complexity estimation at longer timescales requires proper modeling of LRC.
• Revealed significant stress-induced changes in heart period and systolic arterial pressure variability complexity in humans.

Conclusions:

• The proposed parametric approach reliably quantifies multiscale information storage, integrating short-term dynamics and LRC.
• Long-range correlations play a critical role in system complexity across various timescales.
• Findings highlight the differential impact of LRC on physiological variability under stress.