A Practical Approach to Causal Inference over Time

TL;DR

This paper introduces a causal inference framework for dynamical systems over time, linking vector autoregressive models to structural causal models to estimate intervention effects from observational data.

Contribution

It provides a formal connection between VAR models and SCMs for causal inference in time series, enabling estimation of intervention effects from observational data.

Findings

Framework achieves strong forecasting performance

Enables accurate causal effect estimation

Demonstrated on synthetic and real-world data

Abstract

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.