Table 2 Method for causal inference

Method	Multivariate	Nonlinear	Stochastic	Contemporaneous	Leak	Time-delay	Self-causation
CGC²⁶	✓	✗	✓	✗	✗	✓	✓
CTE⁵³	✓	✓	✓	✗	✗	✓	✓
CCM³⁶	✗	✓	✗^a	✓	✗	✗^b	✗
PCMCI²³	✓	✓	✓	✗^c	✗	✓	✓
SURD	✓	✓	✓	✓	✓	✓	✓

List of methods for causal inference investigated, along with the methodological challenges each method is capable of addressing: multivariate relationships, nonlinear dependencies, stochastic (nondeterministic) processes, contemporaneous links, estimation of the causality leak, time-delayed dependencies, and self-causation.
^aCCM aims to reconstruct the attractor manifold associated with two given variables, making it potentially effective for stochastic systems. However, the presence of increased dynamical noise can complicate the reconstruction process.
^bAn extension of the CCM method, extended CCM³⁹, introduces the concept of time-delayed causal interactions.
^cA recent variant of the PCMCI method, PCMCI+⁶², accounts for contemporaneous links.

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