Local Granger Causality

TL;DR

This paper introduces a method to compute local Granger causality, providing a detailed, time-resolved measure of information transfer in Gaussian and complex systems, enhancing understanding of dynamic causal influences.

Contribution

It presents an exact calculation of local Granger causality, linking it to transfer entropy, and offers a fast, robust approach for analyzing information transfer in linear and nonlinear systems.

Findings

Exact calculation of local Granger causality for Gaussian processes

Method applies to both linear stochastic and nonlinear complex systems

Provides a computationally efficient way to analyze time-resolved causal influence

Abstract

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes. We exploit such equivalence and calculate exactly the 'local Granger causality', i.e. the profile of the information transfer at each discrete time point in Gaussian processes; in this frame Granger causality is the average of its local version. Our approach offers a robust and computationally fast method to follow the information transfer along the time history of linear stochastic processes, as well as of nonlinear complex systems studied in the Gaussian approximation.