Appendix A PCMCI Algorithm

The PCMCI algorithm is proposed by Runge et al. [2019], aiming to detect time-lagged causal relations in a window causal graph. There are two stages of PCMCI: the condition-selection stage and the causal discovery stage. In the first stage, unnecessary edges are removed based on the conditional independencies from an initialized partially connected graph where Assumption A4-A5 should be satisfied. In the second stage, Momentary Conditional Independence tests (MCI) are used to further remove the false positive edges caused by autocorrelations in time series data. See Fig.1 for more detail.