Spurious causalities due to low temporal resolution: Towards detection of bidirectional coupling from time series

The detection of causal influences is a topical problem in time series analysis. A traditional approach is based on Granger causality and increasingly often used in very diverse fields. However, a principal possibility of spurious detection of a bidirectional coupling due to low sampling rate, noted by statisticians and econometricians, remains overlooked in physical research. With models widely used in physics, including linear oscillators and nonlinear chaotic maps, we show that spurious coupling characteristics can be rather large and one may even incorrectly identify directionality of a unidirectional coupling if a sampling interval is not small enough. To avoid erroneous conclusions, we suggest a practical test to distinguish between uni- and bi-directional couplings and illustrate it with mathematical systems and climatic data