Complete Characterization for Adjustment in Summary Causal Graphs of Time Series

TL;DR

This paper addresses the problem of determining when causal effects can be identified from observational time series data using summary causal graphs, providing conditions and algorithms for adjustment.

Contribution

It introduces necessary and sufficient conditions for adjustment in summary causal graphs of time series and presents a decision algorithm for identifiability.

Findings

The adjustment criterion is complete in this setting.

A pseudo-linear algorithm is developed for identifiability testing.

Conditions for causal effect identifiability are formally characterized.

Abstract

The identifiability problem for interventions aims at assessing whether the total causal effect can be written with a do-free formula, and thus be estimated from observational data only. We study this problem, considering multiple interventions, in the context of time series when only an abstraction of the true causal graph, in the form of a summary causal graph, is available. We propose in particular both necessary and sufficient conditions for the adjustment criterion, which we show is complete in this setting, and provide a pseudo-linear algorithm to decide whether the query is identifiable or not.