Multiscale Analysis of Information Dynamics for Linear Multivariate Processes

TL;DR

This paper develops an analytical framework for understanding multiscale information dynamics in linear multivariate processes, enabling precise computation of information measures across different temporal scales.

Contribution

It introduces a novel method to analytically compute information dynamics for multiscale linear stochastic processes using state-space models, clarifying theoretical properties.

Findings

Rescaling affects information storage and transfer patterns.

The framework accurately characterizes multiscale information dynamics.

Rescaling can sometimes produce misleading interpretations.

Abstract

In the study of complex physical and physiological systems represented by multivariate time series, an issue of great interest is the description of the system dynamics over a range of different temporal scales. While information-theoretic approaches to the multiscale analysis of complex dynamics are being increasingly used, the theoretical properties of the applied measures are poorly understood. This study introduces for the first time a framework for the analytical computation of information dynamics for linear multivariate stochastic processes explored at different time scales. After showing that the multiscale processing of a vector autoregressive (VAR) process introduces a moving average (MA) component, we describe how to represent the resulting VARMA process using state-space (SS) models and how to exploit the SS model parameters to compute analytical measures of information storage and information transfer for the original and rescaled processes. The framework is then used to quantify multiscale information dynamics for simulated unidirectionally and bidirectionally coupled VAR processes, showing that rescaling may lead to insightful patterns of information storage and transfer but also to potentially misleading behaviors.