41. PCMCI — Time-Series Causal Discovery (Runge et al.)

Type: Constraint-based (time series)
Output: Lagged causal graph (optionally collapsed to base-time DAG)
Reference:
Runge, J. et al. (2019). Detecting causal associations in large nonlinear time series datasets. Science Advances.
Canonical implementation: Tigramite (Runge Lab) — https://github.com/jakobrunge/tigramite

PCMCI is a time-series causal discovery algorithm designed for high-dimensional, autocorrelated data.
Tetrad includes a minimal lagged-edge version for benchmarking, although full practical use is best handled with the Tigramite package.

41.1. Key Idea

PCMCI proceeds in two stages:

  1. PC-style parent pre-selection
    For each target variable Y_t, eliminate candidate parents using conditional independence tests restricted to the strict past (lags >= 1).

  2. MCI (Momentary Conditional Independence) test
    A lagged edge from X_(t–tau) to Y_t is kept if it remains dependent conditional on:

    • the parents of Y_t (excluding X_(t–tau)), plus

    • the parents of X_(t–tau).

Tetrad’s PCMCI only orients lagged edges (tau >= 1) and does not include instantaneous (tau = 0) steps from PCMCI+.

41.2. When to Use

Use PCMCI in Tetrad when:

  • You need lagged causal structure in time-series data.

  • You want to compare Tetrad’s algorithms to a standard baseline for time series.

  • You have moderate-sized data and simple CI tests (e.g., Fisher Z).

Do not rely on the Tetrad version for:

  • PCMCI+ (instantaneous causal effects)

  • nonlinear CI tests

  • large-scale time-series pipelines

Use the Tigramite implementation for those.

41.3. Prior Knowledge Support

PCMCI in Tetrad respects:

  • Forbidden edges

  • Required edges

  • Tiered temporal constraints

  • Any Knowledge object compatible with PC/FCI-style algorithms

41.4. Strengths

  • Designed specifically for time-series causal discovery.

  • Handles autocorrelation via PC-style pre-selection and MCI.

  • More scalable than naive time-series PC.

  • Integrates into Tetrad’s benchmarking and visualization tools.

41.5. Limitations

  • Tetrad version is intentionally minimal:

    • No PCMCI+ instantaneous paths

    • No nonlinear CI tests

    • No advanced false-positive controls from Tigramite

  • Sensitive to:

    • choice of CI test

    • significance level

    • max lag

    • sample size

41.6. Key Parameters in Tetrad

Parameter (camelCase)

Description

maxLag

Maximum lag considered (tau >= 1).

independenceTest

CI test (Fisher Z, etc.).

alpha

Significance level for both phases.

collapse

Collapse lagged edges into a base-time graph.

knowledge

Required/forbidden edges and tier constraints.

verbose

Print detailed logs.

41.7. Reference

Runge, J., Nowack, P., Kretschmer, M., Flaxman, S., & Sejdinovic, D. (2019).
Detecting causal associations in large nonlinear time series datasets.
Science Advances, 5(11).
Tigramite package: https://github.com/jakobrunge/tigramite

41.8. Summary

PCMCI in Tetrad is a time-series causal discovery algorithm using PC-style pre-selection plus the MCI test to recover lagged causal structure.
It is intended for comparisons and educational use, while the full Tigramite implementation should be used for advanced nonlinear or PCMCI+ analyses.