Pattern Causality Analysis

Infer causation from observational data through pattern causality analysis (PC), with original algorithm for time series data from Stavroglou et al. (2020) , as well as methodological extensions for spatial cross-sectional data introduced by Zhang & Wang (2025) , together with a systematic description proposed in Lyu et al. (2026) .

pc

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Pattern Causality Analysis

pc is an R package for pattern-based causality analysis in both time series and spatial cross-sectional data. It uses symbolic pattern representations and cross mapping to detect directional interactions and infer causal structure from temporal dynamics and spatial snapshots. Built on a high-performance C++ backend with a lightweight R interface, pc provides efficient and flexible tools for data-driven causality analysis.

Refer to the package documentation https://stscl.github.io/pc/ for more detailed information.

Installation

Install from CRAN with:

install.packages("pc", dependencies = TRUE)

Install binary version from R-universe with:

install.packages("pc",
                 repos = c("https://stscl.r-universe.dev",
                           "https://cloud.r-project.org"),
                 dependencies = TRUE)

Install from source code on GitHub with:

if (!requireNamespace("pak")) {
    install.packages("pak")
}
pak::pak("stscl/pc", dependencies = TRUE)

References

Sugihara, G., May, R., Ye, H., Hsieh, C., Deyle, E., Fogarty, M., Munch, S., 2012. Detecting Causality in Complex Ecosystems. Science 338, 496–500. https://doi.org/10.1126/science.1227079.

Stavroglou, S.K., Pantelous, A.A., Stanley, H.E., Zuev, K.M., 2019. Hidden interactions in financial markets. Proceedings of the National Academy of Sciences 116, 10646–10651. https://doi.org/10.1073/pnas.1819449116.

Stavroglou, S.K., Pantelous, A.A., Stanley, H.E., Zuev, K.M., 2020. Unveiling causal interactions in complex systems. Proceedings of the National Academy of Sciences 117, 7599–7605. https://doi.org/10.1073/pnas.1918269117.

Zhang, Z., Wang, J., 2025. A model to identify causality for geographic patterns. International Journal of Geographical Information Science 1–21. https://doi.org/10.1080/13658816.2025.2581207.

Lyu, W., Lei, Y., Yi, W., Song, Y., Li, X., Dai, S., Qin, Y., Zhao, W., 2026. Causal discovery in urban data with temporal empirical dynamic modeling: The R package tEDM. Computers, Environment and Urban Systems 127, 102435. https://doi.org/10.1016/j.compenvurbsys.2026.102435.