Discovering Causal Relationships Between Time Series With Spatial Structure

TL;DR

A developing framework that extends time-series causal discovery to systems with spatial structure is introduced, building upon work on causal discovery across contexts and methods for handling spatial confounding in causal effect estimation.

Abstract

Causal discovery is the subfield of causal inference concerned with estimating the structure of cause-and-effect relationships in a system of interrelated variables, as opposed to quantifying the strength of causal effects. As interest in causal discovery builds in fields such as ecology, public health, and environmental sciences where data is regularly collected with spatial and temporal structures, approaches must evolve to manage autocorrelation and complex confounding. As it stands, the few proposed causal discovery algorithms for spatiotemporal data require summarizing across locations, ignore spatial autocorrelation, and/or scale poorly to high dimensions. Here, we introduce a developing framework that extends time-series causal discovery to systems with spatial structure, building upon work on causal discovery across contexts and methods for handling spatial confounding in causal effect estimation. We close by outlining remaining gaps in the literature and directions for future research.

Figures (2)

• Figure 1: An example of a causal graph estimated via constraint-based causal discovery for an observed system $\mathbf{X} = \{X_1, X_2, X_3, X_4, X_5\}$. An edge directed $X_i \rightarrow X_j$ indicates that $X_i$ causes $X_j$. An undirected edge $X_i \mathrel{}X_j$ indicates a causal connection where the direction is unresolvable (i.e. $X_i$ may cause $X_j$ or vice versa).
• Figure 2: Simplified, hypothetical illustrations of systems for which spatiotemporal (A) latent pattern or (B) latent mechanism causal discovery is relevant. A. In this system, arrows show how air pollutants from a volcano eruption causally spread across the world. Modified from Nichol2025. B. In this system, fires cause instantaneous changes in forest cover across Great Britain, which in turn causes changes in a theoretical species' abundance at a time lag. Although the variables are spatially distributed, practitioners seeking to understand causes of an observed shift in species abundance will be more interested in the mechanisms of change between variables than the spatiotemporal patterns of each variable.