Influence of sampling interval on the effect of false coupling between oscillators with different natural oscillation parameters

To analyze the coupling between oscillating systems by time series, the Granger causality assessment–an improved prognosis of the autoregression model–is widely used. It is known that wrong conclusions regarding the presence of bidirectional coupling can be obtained in the case of unidirectional coupled systems when the sampling interval is rather wide. However, it remains unclear under what conditions the effect of false coupling is significant, and thus criteria of significance to account for this effect in practice are absent. In this work, such conditions were studied and qualitatively formulated for an etalon system of coupled oscillators. In particular, it is shown that this effect is negligible in the case of insufficient data if a “fast” oscillator (with a smaller oscillation period and relaxation time) is driving a “slow” oscillator, while the effect is strong otherwise. If both periods are considerably larger than the sampling interval, the effect increases with relaxation time of the driving oscillator and decreases with increasing relaxation time of the driven one.