Local Granger Causality
This work offers a tool for researchers in statistics and complex systems to analyze dynamic information flow, though it is incremental as it builds on existing Granger causality and transfer entropy equivalence.
The authors tackled the problem of tracking information transfer over time in Gaussian processes by introducing 'local Granger causality', which provides a time-point profile of information transfer, with Granger causality as its average. They developed a robust and computationally fast method applicable to linear stochastic processes and nonlinear systems in Gaussian approximation.
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.