February 2024 Characterization of causal ancestral graphs for time series with latent confounders
Andreas Gerhardus
Author Affiliations +
Ann. Statist. 52(1): 103-130 (February 2024). DOI: 10.1214/23-AOS2325


In this paper, we introduce a novel class of graphical models for representing time-lag specific causal relationships and independencies of multivariate time series with unobserved confounders. We completely characterize these graphs and show that they constitute proper subsets of the currently employed model classes. As we show, from the novel graphs one can thus draw stronger causal inferences—without additional assumptions. We further introduce a graphical representation of Markov equivalence classes of the novel graphs. This graphical representation contains more causal knowledge than what current state-of-the-art causal discovery algorithms learn.


I thank Jakob Runge for helpful discussions and suggestions. I thank Tom Hochsprung and Wiebke Günther for careful proofreading and suggestions on how to make the paper more accessible. I thank two anonymous reviewers and two anonymous associate editors for suggestions and questions that helped me to improve the paper.


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Andreas Gerhardus. "Characterization of causal ancestral graphs for time series with latent confounders." Ann. Statist. 52 (1) 103 - 130, February 2024. https://doi.org/10.1214/23-AOS2325


Received: 1 December 2022; Revised: 1 July 2023; Published: February 2024
First available in Project Euclid: 7 March 2024

MathSciNet: MR4718409
Digital Object Identifier: 10.1214/23-AOS2325

Primary: 62A09 , 62D20 , 62M10
Secondary: 68T30 , 68T37

Keywords: ancestral graph , causal discovery , causal graph , Causal inference , latent variable , time series

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.52 • No. 1 • February 2024
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