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Granger causality is well established within the neurosciences for inferenceof directed functional connectivity from neurophysiological data. These datausually consist of time series which subsample a continuous-timebiophysiological process. While it is well-known that subsampling can lead toimputation of spurious causal connections where none exist, here we address theequally important issue of the effects of subsampling on the ability toreliably detect causal connections which do exist.  Neurophysiological processes typically feature signal propagation delays onmultiple time scales; accordingly, we base our analysis on a distributed-lag,continuous-time stochastic model, and consider Granger causality in continuoustime at finite prediction horizons. Via exact analytical solutions, we identifyrelationships among sampling frequency, underlying causal time scales anddetectability of causalities. Our analysis reveals complex interactions betweenthe time scale(s) of neural signal propagation and sampling frequency: wedemonstrate that Granger causality decays exponentially as the sample timeinterval increases beyond causal delay times, identify detectability "blackspots" and "sweet spots", and show that subsampling may sometimes improvedetectability. We also demonstrate that the invariance of Granger causalityunder causal, invertible filtering fails at finite prediction horizons. Wediscuss the implications of our results for inference of Granger causality atthe neural level from various neurophysiological recording modes, and emphasisethat sampling rates for causal analysis of neurophysiological time seriesshould be informed by domain-specific time scales.

Detectability of Granger causality for subsampled continuous-time neurophysiological processes