Time series causal discovery with variable lags

TL;DR

This paper introduces a Tabu-based algorithm for learning time-series causal structures with variable lags, improving accuracy and interpretability in complex dynamic systems.

Contribution

It proposes a novel structure learning method that allows edge-specific lag optimization with theoretical guarantees and scalable parallel implementation.

Findings

Recovered graph structures effectively in simulations.

Estimated lags accurately when adjacencies were correct.

Applied to COVID-19 data, revealed short and long delay dependencies.

Abstract

Causal Bayesian Networks (CBNs) are a powerful tool for reasoning under uncertainty about complex real-world problems. Such problems evolve over time, responding to external shocks as they occur. To support decision-making, CBNs require a cause-and-effect map of the variables under consideration, known as the network's structure. Learning the graphical structure of a causal model from data remains challenging; learning it from time-series data is even harder because dependencies may arise at different time lags. Existing time-series causal discovery methods often assume a fixed lag window and do not explicitly optimise edge-specific lags. We propose a Tabu-based structure learning algorithm that searches for a time-ordered directed structure (i.e., where every edge respects time) while allowing edge-specific lags up to a specified maximum lag. The approach uses a decomposable BIC-based score with node-specific effective sample sizes and an explicit lag-length penalty encouraging parsimonious delay assignments while preserving efficient local score updates. We provide theoretical guarantees of validity and local optimality, and we also describe a parallel implementation for improved scalability. In simulations, the method recovered graph structure competitively and estimated lags accurately when true adjacencies were recovered. On a real-world UK COVID-19 policy dataset, the learnt structure was dominated by short delays while retaining a substantial minority of longer-lag dependencies, consistent with delayed behavioural and epidemiological effects.