Fig. 2.

Stochastic and deterministic model evaluation. Application of causal decomposition to a stochastic system¹⁰ and b deterministic system⁵ (ensemble empirical mode decomposition; EEMD parameter r = 0.15 for both cases). A causal influence was identified in intrinsic mode function (IMF) 2 in both systems, capturing the main mode of signal dynamics in each system (e.g., a lag order of 2 between the IMFs in a, and chaotic behaviour of the logistic model in b). The causal decomposition is not only able to handle noisy data in the stochastic model, but it can also identify causal components in the deterministic model with the aid of EEMD in separating weakly coupled chaotic signals into identifiable IMFs. Data lengths: a 1000 data points; b 400 data points