Granger Causality of Gaussian Signals from Noisy or Filtered Measurements ?

摘要

This paper investigates the assessment of Granger causality (GC) between jointly Gaussian signals based on noisy or filtered measurements. To do so, a recent rank condition for inferring GC between jointly Gaussian stochastic processes is exploited. Sufficient conditions are derived under which GC can be reliably inferred from the second order moments of the noisy or filtered measurements. This approach does not require a model of the underlying Gaussian system to be identified. The noise signals are not required to be Gaussian or independent, and the filters may be noncausal or nonminimum-phase, as long as they are stable.