The Impossible Trinity of Time-Series Validation: A Conservation Law among Training Sufficiency, Test Coverage, and Temporal Causality

Conformal prediction methods enjoy strong theoretical and empirical predictive inference performance, provided the data is exchangeable and is treated symmetrically during training. However, these assumptions are impractical in many settings, such as time series, where temporal dependence violates exchangeability and it is preferable to use predictors that leverage dependence by treating data asymmetrically. Recent work shows that split conformal prediction is robust to these issues, but sample splitting can reduce accuracy, motivating the study of methods that do not rely on data splitting in the time series setting. In this work, we show that the vanilla leave-one-out jackknife can suffer arbitrary loss of coverage even in canonical time series models with mild temporal dependence. As a remedy, we propose a modification tailored to such settings, which we term the leave-a-window-out (LWO) method, and show that it can achieve valid coverage provided that the model-fitting procedure satisfies mild stability properties. Our proofs are based on quantifying the degree to which the data departs from cyclic exchangeability, which we introduce new coefficients to measure. Experiments on time series demonstrate that our method often enjoys valid coverage when the vanilla jackknife fails to cover, while producing much narrower intervals than split conformal prediction.

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 \textbf{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 \emph{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 \emph{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.

Transitioning from bespoke time series models towards time series foundation models changes the relationship of model and application from one-to-one to one-to-many. This shift introduces concentration risk as many, potentially high-risk, forecasting applications are exposed to the same biases and failure modes of a single time series foundation model. At the same time, this centralization allows for economies of scale in model development and validation. In this study we investigate how biases and failure modes of time series foundation models can be identified before deployment. We propose a causal analysis framework to investigate the ability of a time series foundation model to preserve time series patterns. To achieve this, we intervene on parameterized synthetic time series generators and measure the corresponding change in model output under ceteris paribus conditions. We apply our causal analysis framework to Chronos-2 and TimesFM-2.5 and test them across six distinct time series patterns. We find safe configurations for trend and harmonic oscillation patterns. The results also indicate a bias in both models towards overestimating persistence, sudden failures for both models against the regime switch pattern and failure for TimesFM-2.5 against the energy-release pattern. Our review of the original works for both models indicates that the findings might be explained by the data used for pretraining. We conclude our study with suggestions for further model development, recommendations for application-specific model selection, and a discussion of limitations and further research directions.