Technical NoteGranger causality with signal-dependent noise

It is generally believed that the noise variance in in vivo neuronal data exhibits time-varying volatility, particularly signal-dependent noise. Despite a widely used and powerful tool to detect causal influences in various data sources, Granger causality has not been well tailored for time-varying volatility models. In this technical note, a unified treatment of the causal influences in both mean and variance is naturally proposed on models with signal-dependent noise in both time and frequency domains. The approach is first systematically validated on toy models, and then applied to the physiological data collected from Parkinson patients, where a clear advantage over the classical Granger causality is demonstrated.

► Granger causality has been extended to models with signal-dependent noise. ► Granger causality in conditional mean and conditional variance has been unified. ► Causality is analyzed in both the time and the frequency domains. ► Feedback from tremor to brain has been revealed for Parkinson patients.