Interventional Time Series Priors for Causal Foundation Models

Dennis Thumm; Ying Chen

cs.LGMar 11, 2026

Interventional Time Series Priors for Causal Foundation Models

Authors: Dennis Thumm, Ying Chen

Organizations: National University of Singapore · Department of Mathematics, Centre for Quantitative Finance, Risk Management Institute, National University of Singapore

Abstract

Prior-data fitted networks (PFNs) have emerged as powerful foundation models for tabular causal inference, yet their extension to time series remains limited by the absence of synthetic data generators that provide interventional targets. Existing time series benchmarks generate observational data with ground-truth causal graphs but lack the interventional data required for training causal foundation models. To address this, we propose CausalTimePrior, a principled framework for generating synthetic temporal structural causal models (TSCMs) with paired observational and interventional time series. Our prior supports configurable causal graph structures, nonlinear autoregressive mechanisms, regime-switching dynamics, and multiple intervention types (hard, soft, time-varying). We demonstrate that PFNs trained on CausalTimePrior can perform in-context causal effect estimation on held-out TSCMs, establishing a pathway toward foundation models for time series causal inference.

Figures & tables

Generator	Interventions	Nonlinear SCMs	Time-varying Interventions	Regime-switch
CausalTime	✗	✓	—	✗
TimeGraph	✗	✓	—	✗
CAnDOIT	✓ Hard	✓	✗	✗
TECDI	✓ Soft	✗	✗	✗
CaTSG	✓ do -calculus	✓	✗	✗
CausalTimePrior	✓ All	✓	✓	✓

Table 1: Comparison of time series causal data generators. CausalTimePrior is the first to support regime-switching dynamics (changing causal structures over time).

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 1: The three intervention types in CausalTimePrior. Left column: the intervention signal applied to

X_{0}

. Right column: resulting observational (blue) vs. interventional (red) trajectories. Yellow shading marks the intervention window

[30,70)

Figure 2: Four time-varying intervention profiles. Blue: observational trajectory. Red: interventional trajectory. Dashed: intervention signal

c(t)

(right axis). All four profiles are applied to the same variable in the same TSCM.

Figure 3: Paired observational and interventional time series for the intervention target variable. The yellow shaded region indicates the intervention period. The divergence between blue (observational) and red (interventional) trajectories demonstrates the causal effect of the intervention.

Figure 4: All variables in a sampled 6-variable TSCM with a hard intervention on Variable 4. The intervention target is highlighted with a yellow background. Causal effects propagate through the graph structure, affecting downstream variables while leaving non-causally connected variables unchanged.

Figure 5: Distributions of prior properties across 100K sampled TSCMs from CausalTimePrior. The prior produces diverse graph structures, intervention types, and effect magnitudes.

Query Type	Queries	RMSE $\downarrow$	NMSE $\downarrow$	Mean Pred	Mean GT	Pred/GT $\uparrow\downarrow=1$
Intervened	573	226.39	1.41	33.91	35.68	0.95
Downstream	270	231.31	0.67	57.50	67.70	0.85
Non-causal	157	143.15	0.66	15.66	33.99	0.46
Overall	1000	216.87	0.99	37.41	44.06	0.85

Appendix

Table 2: Three-way evaluation on held-out TSCMs. NMSE (Normalized MSE = MSE/Var(GT); NMSE

<

1 is better than predicting the mean). The model’s Pred/GT ratio is highest for intervened queries (0.95) and lowest for non-causal queries (0.46), suggesting learned causal understanding. Overall NMSE

\approx

1.0 indicates limited absolute prediction quality.

Method	RMSE $\downarrow$	MAE $\downarrow$	Effect Dir. Acc. $\uparrow$	Effect Size Corr. $\uparrow$
Oracle	0.00	0.00	100.0%	1.000
PCMCI+	161.38	28.67	74.1%	0.784
SimpleCausalPFN	176.45	34.92	70.4%	0.821
VAR-OLS	176.45	33.86	93.7%	0.821
Mean Prediction	256.18	73.26	60.4%	0.286

Appendix

Table 3: Comparison with baselines on held-out TSCMs. SimpleCausalPFN achieves comparable RMSE to VAR-OLS while requiring no per-dataset fitting. PCMCI+ achieves the lowest RMSE but requires per-sample causal graph discovery.

Model	RMSE $\downarrow$	MAE $\downarrow$	Effect Dir. Acc. $\uparrow$	Effect Size Corr. $\uparrow$
Mixed (100K)	216.87	81.68	70.4%	0.821
Hard-only (10K)	212.16	69.68	63.9%	0.691

Appendix

Table 4: Intervention type ablation. The mixed-intervention model achieves higher effect direction accuracy and effect size correlation compared to the hard-only model.

Test Set	RMSE $\downarrow$	NMSE $\downarrow$	MAE $\downarrow$	Effect Dir. Acc. $\uparrow$	Effect Size Corr. $\uparrow$
In-distribution	216.87	0.99	81.68	70.4%	0.821
OOD	265.97	0.72	163.25	62.7%	0.599

Appendix

Table 5: Out-of-distribution generalization. Performance degrades on OOD TSCMs with larger, denser graphs and complex mechanisms, but the model retains basic causal structure (downstream RMSE

>

intervened RMSE).

Causal Foundation Models

Causal foundation models are pretrained models that discover causal graphs or estimate effects on new datasets using data and causal assumptions.

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Jul 29, 2026J/K move · Enter open · S save

DoTime: A Synthetic Benchmark Generator for Interventional and Counterfactual Time Series

Dennis Thumm, Billy Tim Anthony, Ying Chen

National University of Singapore, Singapore, Singapore

Counterfactual Evaluation Structural Causal Models Time-Series Causal Discovery Causal Counterfactual Generation Synthetic Benchmark Generation Causal Intervention

Open paper AskPDF arXiv

Most benchmarks for causal inference over time series are observational, small, or domain-specific, leaving interventional and counterfactual estimation under-served exactly where it matters most, such as in healthcare, policy evaluation, and climate science. We introduce DoTime, an open, scalable, and theoretically grounded generator of multivariate temporal structural causal models (TSCMs) with interventions, released as the \code{dotime} PyPI package together with four frozen evaluation suites. Beyond existing work, it adds capabilities absent from prior generators: continuous-time intervention windows, counterfactual sampling modes with a positivity guard, regime-switching SCMs as a strict generalization of interrupted time series, non-stationary dynamics by construction with switching SCM parameters, and deterministic ramp and sinusoidal intervention profiles that place trends and structural breaks inside the evaluation window. Moreover, it demonstrates the suitability of the generator as a prior for a causal foundation model reference implementation. The released suites span a training-scale snapshot of

100{,}000

trajectories and eight named identification structures, each with exact ground truth: paired interventional trajectories from the same SCM throughout, and shared-noise counterfactuals in the continuous-time suite. We ship reference baseline implementations with an evaluation harness, and pose a falsifiable claim: interventional training buys a measurable direction-accuracy advantage over an observational model of identical capacity. It is tested across three training seeds per arm. Under structure-matched evaluation on held-out episodes, the interventional prior-fitted network's (PFN) gap is positive in every structure, trajectory length, and seed tested.

Abstract

Causal Foundation Models

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