# A Practical Approach to Causal Inference over Time

arXiv: https://arxiv.org/abs/2410.10502 · HTML: https://mlsanity.com/paper/2410.10502/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [From Ordinary Differential Equations to Structural Causal Models: the deterministic case](https://mlsanity.com/paper/1408.2063/) (2014)
- [An Analysis of Linear Time Series Forecasting Models](https://mlsanity.com/paper/2403.14587/) (2024)
- [Causal Inference by Identification of Vector Autoregressive Processes with Hidden Components](https://mlsanity.com/paper/1411.3972/) (2014)
- [Comparative Study of Causal Discovery Methods for Cyclic Models with Hidden Confounders](https://mlsanity.com/paper/2401.13009/) (2024)

## Built on by (most cited first, 4 of 4)

- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [Causal Structure Learning for Dynamical Systems with Theoretical Score Analysis](https://mlsanity.com/paper/2512.14361/) (2025)
- [When Counterfactual Reasoning Fails: Chaos and Real-World Complexity](https://mlsanity.com/paper/2503.23820/) (2025)
- [Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems](https://mlsanity.com/paper/2603.08311/) (2026)

## Abstract (arXiv)

In this paper, we focus on estimating the causal effect of an intervention over time on a dynamical system. To that end, we formally define causal interventions and their effects over time on discrete-time stochastic processes (DSPs). Then, we show under which conditions the equilibrium states of a DSP, both before and after a causal intervention, can be captured by a structural causal model (SCM). With such an equivalence at hand, we provide an explicit mapping from vector autoregressive models (VARs), broadly applied in econometrics, to linear, but potentially cyclic and/or affected by unmeasured confounders, SCMs. The resulting causal VAR framework allows us to perform causal inference over time from observational time series data. Our experiments on synthetic and real-world datasets show that the proposed framework achieves strong performance in terms of observational forecasting while enabling accurate estimation of the causal effect of interventions on dynamical systems. We demonstrate, through a case study, the potential practical questions that can be addressed using the proposed causal VAR framework.