Table S1.

Nonzero parameters for VAR(3) three-node series system of example 1

System component	Nonzero parameter	True value	Order 3 mean (SD)	Order 6 mean (SD)	Order 20 mean (SD)
	$A_{1\mathit{\text{,}}1}\left(1\right)$	−0.900	−0.900	−0.900	−0.899
Node 1 dynamics			(0.044)	(0.045)	(0.047)
	$A_{1\mathit{\text{,}}1}\left(2\right)$	−0.810	−0.809	−0.813	−0.812
			(0.053)	(0.063)	(0.066)
	$A_{2\mathit{\text{,}}2}\left(1\right)$	1.212	1.211	1.211	1.211
Node 2 dynamics			(0.044)	(0.047)	(0.050)
	$A_{2\mathit{\text{,}}2}\left(2\right)$	−0.490	−0.490	−0.490	−0.492
			(0.062)	(0.075)	(0.079)
	$A_{3\mathit{\text{,}}3}\left(1\right)$	−1.212	−1.212	−1.212	−1.212
Node 3 dynamics			(0.042)	(0.046)	(0.049)
	$A_{3\mathit{\text{,}}3}\left(2\right)$	−0.640	−0.640	−0.643	−0.644
			(0.059)	(0.072)	(0.078)
	$A_{2\mathit{\text{,}}1}\left(1\right)$	−0.356	−0.355	−0.355	−0.354
			(0.045)	(0.046)	(0.048)
Channel 1 to 2	$A_{2\mathit{\text{,}}1}\left(2\right)$	0.714	0.714	0.714	0.715
			(0.052)	(0.062)	(0.065)
	$A_{2\mathit{\text{,}}1}\left(3\right)$	−0.356	−0.355	−0.356	−0.354
			(0.070)	(0.084)	(0.090)
	$A_{3\mathit{\text{,}}2}\left(1\right)$	−0.310	−0.311	−0.310	−0.311
			(0.044)	(0.046)	(0.049)
Channel 2 to 3	$A_{3\mathit{\text{,}}2}\left(2\right)$	0.500	0.501	0.501	0.502
			(0.062)	(0.074)	(0.078)
	$A_{3\mathit{\text{,}}2}\left(3\right)$	−0.310	−0.313	−0.313	−0.313
			(0.039)	(0.079)	(0.085)
Noise 1	${\mathrm{\Sigma }}_{1\mathit{\text{,}}1}$	1	1.000	1.000	1.000
			(0.067)	(0.069)	(0.073)
Noise 2	${\mathrm{\Sigma }}_{2\mathit{\text{,}}2}$	1	1.000	1.000	1.000
			(0.064)	(0.065)	(0.069)
Noise 3	${\mathrm{\Sigma }}_{3\mathit{\text{,}}3}$	1	1.002	1.002	1.002
			(0.063)	(0.064)	(0.068)