Table 1.

Detection of true and false effective connectivity for a fixed embedding dimension d of 7, and an embedding delay τ of 1 autocorrelation time

Dynamics	δ	Coupling	u	X →Y	Y →X
				True	False
AR(10)	5	Lin	6	1	1
AR(10)	5	Lin	21	1	0
AR(10)	5	Lin	101	0	0
AR(10)	5	Threshold	6	1	1
AR(10)	5	Threshold	21	1	0
AR(10)	5	Threshold	101	0	0
AR(10)	5	Quadratic	6	1	1
AR(10)	5	Quadratic	21	1	0
AR(10)	5	Quadratic	101	0	0
AR(10)	20	Lin	6	1	1
AR(10)	20	Lin	21	1	0
AR(10)	20	Lin	101	1	0
AR(10)	20	Threshold	6	0	0
AR(10)	20	Threshold	21	1	0
AR(10)	20	Threshold	101	0	0
AR(10)	20	Quadratic	6	0	0
AR(10)	20	Quadratic	21	1	0
AR(10)	20	Quadratic	101	0	0
AR(10)	100	Lin	6	1	0
AR(10)	100	Lin	21	1	0
AR(10)	100	Lin	101	1	0
AR(10)	100	Threshold	6	0	0
AR(10)	100	Threshold	21	0	0
AR(10)	100	Threshold	101	1	0
AR(10)	100	Quadratic	6	1	0
AR(10)	100	Quadratic	21	1	0
AR(10)	100	Quadratic	101	1	0

Given is the detected effective connectivity in dependence of the parameter prediction time u for data with different interaction delays δ of 5, 20, and 100 samples. Data were simulated with autoregressive order ten dynamics and unidirectional coupling X →Y via three different coupling functions (linear, threshold, quadratic). Simulation results based on 120 trials. Note: false positives emerge for short interaction delays δ, i.e. the inclusion of more recent samples of X, i.e. samples that are just before the earliest embedding time-point; false positives in these cases are suppressed using a larger prediction time, i.e. moving the embedding of X and the samples of X that are transferred to Y further into the past; short interaction delays can robustly be detected with prediction times that are longer than the interaction delay, if the difference is not excessive