Assessing Connectivity in the Presence of Instantaneous Causality
This chapter is devoted to a discussion of the impact of instantaneous causality on the computation of frequency domain connectivity measures. Instantaneous causality (IC) refers to interactions between two observed time series which occur within the same time lag. While IC is hard to interpret in real-world physical systems because causal interactions take time to occur in these systems, it becomes a clear concept when time-series models are used to describe physical interactions in practice. In fact, instantaneous effects show up in practical time-seriesmodeling anytime the time resolution of themeasurements is lower than the time scale of the lagged causal influences occurring among the processes underlying the measured time series. This situation is
likely encountered in experimental time-series analysis and, in particular, cannot be ignored in the study of brain connectivity.