Impact of Sampling Effects in Granger Causality Inference

Most dynamical processes are continuous in time, whereas in experiment, signals are often measured in the form of discrete time series and conclusions are drawn by analyzing these sampled signals. Whether such empirical data inference is dependent on sampling interval is an important issue arising from many scientific fields, we have shown that, for both linear and nonlinear processes, the computed Granger causality (GC) is dependent on the sampling interval length and have provides an approach to extract the intrinsic causal properties from continuous processes, thus leading to a reliable GC inference.

We construct several idealized linear models to illustrate possible mechanisms underlying the sampling artifacts on the Granger causality analysis: (i) oscillations, often vanishing at certain finite sampling interval lengths, (ii) the GC vanishes linearly as one uses finer and finer sampling. From these models, we show that these sampling effects can occur in both linear and non-linear dynamics and how the spectral structures of signals gives rise to these sampling effects.