Multiscale analysis of information dynamics for linear multivariate processes.

Area of Science:

• Complex Systems Analysis
• Information Theory
• Stochastic Processes

Background:

• Multivariate time series analysis is crucial for understanding complex physical and physiological systems.
• Information-theoretic methods are increasingly used for multiscale analysis, but their theoretical properties remain unclear.
• Understanding system dynamics across temporal scales is a significant challenge.

Purpose of the Study:

• To introduce a framework for the analytical computation of information dynamics in linear multivariate stochastic processes at different time scales.
• To address the poorly understood theoretical properties of information-theoretic measures in multiscale analysis.
• To provide a method for quantifying information storage and transfer in rescaled processes.

Main Methods:

• Demonstrated that multiscale processing of vector autoregressive (VAR) processes introduces a moving average (MA) component.
• Represented the resulting VARMA processes using state-space (SS) models.
• Utilized SS model parameters to compute analytical measures of information storage and transfer.

Main Results:

• Developed a framework for analytical computation of information dynamics for linear multivariate stochastic processes.
• Quantified multiscale information dynamics in simulated unidirectionally and bidirectionally coupled VAR processes.
• Observed that rescaling can reveal insightful patterns in information storage and transfer.

Conclusions:

• The developed framework enables analytical computation of information dynamics across multiple time scales.
• Rescaling time series data can yield valuable insights into system information dynamics.
• Caution is advised as rescaling may also lead to potentially misleading interpretations of information storage and transfer.