The influence of observational noise on the effect of spurious coupling between oscillators as estimated from their time series

The conventional practice of establishing the structure of coupling between the elements of complex systems from experimental observations of their oscillations (time series) treated in terms of the Wiener–Granger causality revealed some problems of measurement noise hindering the obtaining of reliable results. In particular, the presence of observational noise can produce the effect of spurious coupling (SC) that leads to the erroneous conclusion that there is mutual (bidirectional) coupling between two elements that are in fact coupled unidirectionally. A quantitative analysis of this phenomenon has been carried out, and recommendations are given how to reduce the probability of error. It is shown that the SC effect is usually manifested only in the presence of strong noise comparable with the level of observed oscillations, although rare situations are possible in which the SC effect takes place at much lower noises.