nucleation

LIT-1164: Causal Reasoning in Graphical Time Series Models

2 min read

Properties5
StatusActive — read in full 2026-10-16 (NOTE-941); worth reading as the short statement of exactly when a Granger-causal analysis says something about interventions: under its intervention assumptions, which need the series to include every relevant process (observed or not) and exclude instantaneous causation, a missing Granger edge means no causal effect at the next step and non-ancestry means none at any horizon, and time-series back-door and front-door criteria identify effects from observational data. Read it knowing that the front-door theorem's proof is deferred to a paper "in preparation", that the results are sufficient conditions, and that the examples are Gaussian VARs. Filed as THEORY-704.
Tagscausality, mathematical-statistics
ExtendsLIT-1173 — Investigating Causal Relations by Econometric Models and Cross-spectral Methods
Cited as “paper” byNOTE-941 — Eichler and Didelez — Causal reasoning in graphical time series models
Cited as “source” byTHEORY-704 — In a stationary multivariate time series whose components include every relevant process, with interventions that are isolated exogenous changes and no instantaneous causation, a missing Granger-causal edge from a to b means intervening on a has no effect on b at the next step, non-ancestry means no effect at any horizon, and a set whose observed past blocks every back-door path into b's ancestors identifies the effect from observational data, as a multi-step linear-predictor coefficient in the Gaussian case

Graph View

Michael Eichler and Vanessa Didelez (2007), “Causal Reasoning in Graphical Time Series Models”, Proceedings of the 23rd Conference on Uncertainty in Artificial Intelligence: 109–116 — ARXIV-1206.5246

Key takeaways

From the reading, NOTE-941.

  • Causality as intervention (Defs. 2.1, 2.5). The causal effect of Xa(t) on Xb(t + h) is the mean of Xb(t + h) under an intervention regime σa(t): atomic, conditional on the past, or random.
  • The assumptions that do the work (Assumption 2.3). (i) Whether one intervenes in Xa(t) is independent of the past of the whole system and of the other variables at t, which excludes instantaneous causality. (ii) The future depends on the intervention only through the system’s present and past. They hold only if the system V includes every relevant process, observed or not, and the paper says they must be checked in each application.
  • Granger to intervention (Lemma 4.10, Conclusion). If X satisfies the global Granger-causal Markov property for a mixed graph, a missing edge a → b means Xa(t) has no effect on Xb(t + 1), and a ∉ an(b) means no effect at any horizon. A present edge is only “potentially causal”.
  • Identification (Theorems 3.1, 4.11, 4.13). A set S whose observed past blocks every an(b)-pointing back-door path identifies the effect from observational quantities. With S = V this always holds, by (ii). A front-door criterion covers a latent confounder (Example 4.14); its proof is deferred.
  • Gaussian case (Example 3.2). The identified effect of setting Xa(t) = x* is Φ_ba^{(h)}(1)x*, a coefficient of the best linear h-step predictor from S’s autoregression.

Standing in the record

Filed on 2026-10-16 to check NOTE-010’s C5, and read the same day. It qualifies C5. Measuring every relevant variable is one of the conditions, not all of them. Instantaneous causality must also be absent, and interventions must be exogenous changes of the system. Even then, the result is that Granger noncausality implies no intervention effect, and that the effect is identified from the observational predictor. It does not make the two analyses one analysis. Filed as THEORY-704; the record’s own statement is CLAIM-333.

Backlinks