causal impact analysis

This paper bridges the theoretical and practical gap between the potential outcomes framework and causal graphical models. Addressing core causal inference problems—including counterfactual reasoning, treatment effect identification, and estimation—the work systematically unifies potential outcomes, causal diagrams, d-separation, the backdoor criterion, single-world intervention graphs (SWIGs), and structural equation models, offering the first coherent account of their logical interconnections. Methodologically, it proposes a robust identification strategy grounded in propensity score estimation and inverse probability weighting, augmented with sandwich standard errors for valid statistical inference. The key contribution is a pedagogically transparent, operationally feasible framework that lowers the barrier to integrating these two dominant causal paradigms. By harmonizing conceptual rigor with practical applicability, the paper provides applied researchers with an accessible yet theoretically sound entry point into modern causal inference. (149 words)

Existing time series benchmarks lack interventional data, hindering the training of causal foundation models. To address this gap, this work proposes CausalTimePrior, a framework that introduces the first synthetic time series structural causal model (TSCM) capable of generating paired observational and interventional data. The framework supports configurable causal graphs, nonlinear autoregressive mechanisms, state-switching dynamics, and diverse intervention types—including hard, soft, and time-varying interventions. Prior-data fitting networks (PFNs) trained within this framework demonstrate effective in-context estimation of causal effects on unseen TSCMs, underscoring the framework’s pivotal role in advancing causal foundation models for time series.

Traditional causal inference methods struggle to capture how interventions affect the dynamic evolution of time series, such as persistence and transition patterns. This work extends the potential outcomes framework to path space and introduces the Dynamic Average Treatment Effect (DATE) to characterize how causal effects evolve over time. It establishes the first dynamic causal inference framework in path space, develops a dynamic inverse probability weighting estimator suitable for observational data, and reveals that, under sparse treatment regimes, the conditional mean trajectory admits a linear state-space structure. Simulations demonstrate that the proposed method accurately captures dynamic effects that static approaches systematically misestimate. In an empirical application to COVID-19 lockdown policies, the method successfully estimates and decomposes the treatment effects over time.

This paper addresses the identification of causal effects in time-series data under latent confounding, without relying on instrumental variables or negative controls. We propose the first linear identification framework grounded in structural vector autoregression (SVAR) and the full-time graph. Leveraging Wright’s path tracing rules and covariance algebra, we derive sufficient conditions—comprising graphical structure constraints and lag-order criteria—for the identifiability of both direct and total causal effects, assuming only knowledge of the temporal structure. We formally prove that, under these conditions, the causal parameters are uniquely identifiable. Numerical experiments demonstrate the method’s accuracy, robustness to model misspecification, and substantial improvement in feasibility for settings where no auxiliary variables are available.

This work addresses a key limitation in existing time series causal discovery methods, which typically assume a fixed lag order and thus struggle to capture variable-lag dependencies. The authors propose a Tabu search–based structure learning algorithm that independently optimizes the lag order for each causal edge while respecting temporal ordering constraints. By introducing a decomposable BIC scoring function that incorporates both effective sample size per node and a penalty for lag length, the method guarantees local optimality in theory and supports parallelization for improved scalability. Experiments demonstrate that the approach accurately recovers graph structures and precisely estimates lags in synthetic data. When applied to UK COVID-19 policy data, it identifies causal relationships dominated by short lags yet also exhibiting longer-lag effects, aligning well with established epidemiological principles.

This work addresses the challenge of causal discovery in high-dimensional, nonstationary multivariate time series by introducing an open-source Python library that integrates, for the first time, a unified GPU-accelerated conditional independence testing layer, plug-in structural change-point detection, and multiple causal discovery algorithms—including CDNOTS, GES, Granger causality, and LASSO-VAR—to enable piecewise causal modeling and end-to-end causal effect estimation. Implemented in PyTorch for computational efficiency, the library supports Python 3.10–3.12, offers a command-line interface, and seamlessly integrates with DoWhy. Released publicly on GitHub, this tool significantly enhances the scalability and usability of causal analysis for nonstationary time series data.

This study addresses the limitations of traditional control-based causal inference methods—such as matching and difference-in-differences—in settings characterized by pervasive or structurally ambiguous spillover effects, where reliance on uncontaminated control units impedes accurate identification of both average direct and spillover effects. Within the potential outcomes framework, this work provides the first systematic comparison between control-based and prediction-based counterfactual approaches—including interrupted time series and machine learning control—in terms of their identification capabilities. Through simulation and empirical analyses, the authors demonstrate that in environments with widespread interference, prediction-based methods can more reliably estimate certain causal parameters over short horizons, circumventing the stringent assumption of unperturbed units and thereby offering a promising alternative for causal inference under complex interference.

This study addresses the critical need for timely detection of performance degradation following marketing interventions, a task for which the sensitivity of existing Bayesian causal impact models in early monitoring remains unclear. The authors develop a simulation-based evaluation framework that systematically assesses the models’ alerting capability under varying effect sizes, confidence levels, and monitoring windows by perturbing daily traffic data along an abandonment-recovery marketing journey. Their work extends causal impact analysis from retrospective estimation to real-time monitoring, introducing a quantifiable method to evaluate detection sensitivity and revealing distinct behavioral patterns between proportional and sustained alerting criteria in dynamic environments. Results demonstrate that detection performance is highly dependent on the interaction among these three factors, with sustained criteria exhibiting greater stability and operational practicality over longer monitoring windows.

Traditional sensitivity analyses in causal inference often rely on worst-case assumptions that conflict with real-world priors and yield uninformative conclusions. This work proposes the Bayesian Sensitivity Value (BSV), which integrates real-world evidence–informed priors into the s-value framework and employs Bayesian inference with Monte Carlo approximation to quantify the expected sensitivity of causal estimates under perturbations. Applied to an observational study examining the effect of diabetes treatment on body weight, BSV demonstrates that conventional worst-case analyses frequently rest on implausible data-generating mechanisms, thereby offering a more realistic and informative assessment of sensitivity.