Table 1 List of methods, key strengths, and further research directions addressing current limitations

Granger causality and nonparametric extensions^9,37,99

Significance assessment; nonparametric versions

Dealing with contemporaneous effects and feedback cycles; high-dimensionality; deterministic dependencies; synergistic effects; time scales; unobserved variables

Nonlinear state-space methods^10,11

State-dependent nonlinear systems; contemporaneous effects

Significance assessment; high-dimensionality; highly synchronous dynamics; high stochasticity; time scales; unobserved variables

Conditional independence-based algorithms¹²

High-dimensionality; unobserved variables; nonparametric tests

Significance assessment; deterministic effects; synergistic effects; time scales; contemporaneous feedback cycles

PCMCI^23,24

High-dimensionality; time delays; strong autocorrelation; nonparametric tests

Unobserved variables; deterministic effects; synergistic effects; time scales; contemporaneous feedback cycles

Information-theoretic algorithms^23,24,51

High-dimensionality; nonparametric; time delays; information-theoretic interpretation

Significance assessment; unobserved variables; deterministic effects; synergistic effects; time scales; contemporaneous feedback cycles; efficient entropy estimation

Structural causal models^13,38

Contemporaneous effects; nonparametric versions

High-dimensionality; synergistic effects; time scales; unobserved variables; time delays

Invariance-based methods^{4,13,57,58,60,61}

Utilizes heterogeneity in space and time

Causality in stationary regimes; same as for SCMs

Bayesian score-based approaches⁴⁸

Bayesian uncertainty assessment; inclusion of expert knowledge

High-dimensionality; nonlinearity; deterministic effects; synergistic effects; time scales; contemporaneous feedback cycles; unobserved variables; combine with cond. independence-based methods¹⁰⁰