Causal Foundation Models for Time Series based on Prior-Data fitted Networks

Foundation models trained on synthetic data have recently transformed tabular machine learning and time series forecasting, with Prior-Data Fitted Networks (PFNs) being the leading approach. Causal Foundation Models (CFMs) extend the PFN paradigm from prediction to causal effect estimation. However, existing CFMs are limited to static (i.i.d.) settings and do not address the challenges posed by temporal data. In this work, we extend the PFN framework to estimate causal effects in time series. We identify prior-design criteria and introduce a novel temporal causal PFN prior that yields data with meaningful causal effects while maintaining the stability of sampled trajectories. Furthermore, we provide theoretical results that shed light on the asymptotic behaviour of the conditional interventional distribution implied by a temporal causal prior. Empirically, we find that PFNs can successfully learn to estimate causal effects in temporal settings, achieving promising performance on synthetic data covering the back-door and front-door settings.