This study compares two causal methods, the Liang–Kleeman information flow (LKIF) and the Peter and Clark momentary conditional independence (PCMCI), applied to four artificial models of increasing complexity and a real-world case study using climate indices. The primary goal is to evaluate the performance of these methods in identifying true causal links compared to classical correlation analysis. **Artificial Models:** 1. **2D Model:** LKIF accurately identifies the causal link from \(x_2\) to \(x_1\) and the absence of reverse influence, while PCMCI fails to detect any significant causal influence due to the small time step. 2. **6D Model:** Both LKIF and PCMCI correctly identify all seven causal links, but PCMCI's performance improves with a larger time step. 3. **9D Model:** LKIF and PCMCI can detect all correct causal links with appropriate lags, although some weak influences are identified by both methods. 4. **Lorenz (1963) Model:** LKIF and PCMCI detect a two-way causal link between \(x\) and \(y\), and LKIF also identifies a strong two-way causal link between \(x^2\) and \(z\). **Real-World Case Study:** - **Climate Indices:** Both methods identify similar causal links, such as the influence of the Arctic Oscillation (AO) on the Pacific Decadal Oscillation (PDO) and the Tropical North Atlantic (TNA) index. However, LKIF identifies additional causal links, such as the influence of the AO on the North Atlantic Oscillation (NAO) and the Quasi-Biennial Oscillation (QBO), which PCMCI does not detect. - **Lag Analysis:** For the Lorenz model, both methods show lag-dependent causal relationships, with LKIF and PCMCI detecting different lags for the same causal links. **Conclusion:** LKIF and PCMCI outperform classical correlation analysis in identifying true causal links, especially in complex systems. LKIF is better with fewer variables and smaller time steps, while PCMCI performs better with more variables and larger lags. Further research is needed to confirm these findings, particularly in nonlinear causal methods.This study compares two causal methods, the Liang–Kleeman information flow (LKIF) and the Peter and Clark momentary conditional independence (PCMCI), applied to four artificial models of increasing complexity and a real-world case study using climate indices. The primary goal is to evaluate the performance of these methods in identifying true causal links compared to classical correlation analysis. **Artificial Models:** 1. **2D Model:** LKIF accurately identifies the causal link from \(x_2\) to \(x_1\) and the absence of reverse influence, while PCMCI fails to detect any significant causal influence due to the small time step. 2. **6D Model:** Both LKIF and PCMCI correctly identify all seven causal links, but PCMCI's performance improves with a larger time step. 3. **9D Model:** LKIF and PCMCI can detect all correct causal links with appropriate lags, although some weak influences are identified by both methods. 4. **Lorenz (1963) Model:** LKIF and PCMCI detect a two-way causal link between \(x\) and \(y\), and LKIF also identifies a strong two-way causal link between \(x^2\) and \(z\). **Real-World Case Study:** - **Climate Indices:** Both methods identify similar causal links, such as the influence of the Arctic Oscillation (AO) on the Pacific Decadal Oscillation (PDO) and the Tropical North Atlantic (TNA) index. However, LKIF identifies additional causal links, such as the influence of the AO on the North Atlantic Oscillation (NAO) and the Quasi-Biennial Oscillation (QBO), which PCMCI does not detect. - **Lag Analysis:** For the Lorenz model, both methods show lag-dependent causal relationships, with LKIF and PCMCI detecting different lags for the same causal links. **Conclusion:** LKIF and PCMCI outperform classical correlation analysis in identifying true causal links, especially in complex systems. LKIF is better with fewer variables and smaller time steps, while PCMCI performs better with more variables and larger lags. Further research is needed to confirm these findings, particularly in nonlinear causal methods.