Dynamic causal inference with time series data

2026-01-31

AI Summary

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.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We generalize the potential outcome framework to time series with an intervention by defining causal effects on stochastic processes. Interventions in dynamic systems alter not only outcome levels but also evolutionary dynamics -- changing persistence and transition laws. Our framework treats potential outcomes as entire trajectories, enabling causal estimands, identification conditions, and estimators to be formulated directly on path space. The resulting Dynamic Average Treatment Effect (DATE) characterizes how causal effects evolve through time and reduces to the classical average treatment effect under one period of time. For observational data, we derive a dynamic inverse-probability weighting estimator that is unbiased under dynamic ignorability and positivity. When treated units are scarce, we show that conditional mean trajectories underlying the DATE admit a linear state-space representation, yielding a dynamic linear model implementation. Simulations demonstrate that modeling time as intrinsic to the causal mechanism exposes dynamic effects that static methods systematically misestimate. An empirical study of COVID-19 lockdowns illustrates the framework's practical value for estimating and decomposing treatment effects.

Problem

• dynamic causal inference
• time series
• intervention
• stochastic processes
• causal effects

Innovation

• Dynamic Causal Inference
• Potential Outcomes
• Time Series
• Dynamic Average Treatment Effect
• State-Space Model