One Thing Leads to Another: The Essentials of Time Series Causal Discovery

Kurt Butler; Damian Machlanski; Michael P. J. Camilleri; Zhihua Liu; Panagiotis Dimitrakopoulos; Feng Chen; Ricardo Silva; Sotirios A. Tsaftaris

eess.SPOct 9, 2026

One Thing Leads to Another: The Essentials of Time Series Causal Discovery

Authors: Kurt Butler, Damian Machlanski, Michael P. J. Camilleri, Zhihua Liu, Panagiotis Dimitrakopoulos, Feng Chen, Ricardo Silva, Sotirios A. Tsaftaris

Organizations: School of Engineering, The University of Edinburgh, and the Causality in Healthcare AI Hub (CHAI) · School of Informatics, The University of Edinburgh and CHAI · Department of Statistical Science, University College London, and CHAI

Abstract

Time series causal discovery --- the process of detecting causation between time series --- has its roots in signal processing research from over a half century ago. It has since received active and widespread interest, evolving into different forms across domains such as statistics, dynamical systems and machine learning. Entering this fragmented and constantly evolving research landscape can be daunting. This tutorial provides a unified overview of time series causal discovery across research communities. We introduce the key principles invoked by modern discovery methods, and we discuss their limitations and assumptions. We also discuss how discovery methods are evaluated, benchmarked and fine-tuned. We further discuss how causal discovery for time series is becoming crucial for downstream tasks in agriculture and Earth science, in healthcare, and in artificial intelligence systems. We believe that this tutorial will serve as a valuable resource in navigating the deluge of recent causality research, as well as an invitation to signal processing audiences to contribute to causal problems. To further help readers, we host a companion repository to link to useful code packages and resources at https://github.com/CHAI-UK/Awesome-Time-Series-Causal-Discovery.

Figures & tables

Panel of Figure 1 — Fig. 1: Three ways to graphically represent causality between time series. Unlike Full Graphs and Window Graphs, Summary Graphs are permitted to have cycles.

Fig. 2: A visual taxonomy of common inference principles for TSCD . Given a definition of causality, there are often several candidate principles for detecting causation. Compare with Table I to see example methods for each inference principle. This taxonomy does not exhaustively show every principle, and there exist methods which are hybrids of multiple inference principles.

Principle	Example Method(s)	Graph Type	Dynamics	Causal Sufficiency
Granger causality	Linear Granger Causality (GC) [ 1 ]	Summary	Stochastic	Assumed
Granger causality	Neural GC [ 9 ]	Summary	Stochastic	Assumed
Information-theoretic	Transfer entropy [ 10 ]	Summary	Stochastic	Assumed
Cross mapping	CCM [ 6 ]	Summary	Deterministic	Relaxed
Constraint-based	PCMCI [ 11 ]	Window	Stochastic	Assumed
Constraint-based	LPCMCI [ 12 ]	Window	Stochastic	Relaxed

TABLE I: Some representative TSCD methods from each inference principle and a comparison of their key assumptions.

Metric	Range	Target	Intuition
Precision	$[0,1]$	$\uparrow$	Avoiding false causal links
Recall	$[0,1]$	$\uparrow$	Detecting existing causal links
F1	$[0,1]$	$\uparrow$	Recall-Precision balance
SHD	$[0,p^{2}]$	$\downarrow$	Number of structural errors
SID	$[0,p(p-1)]$	$\downarrow$	Number of causal effect errors

TABLE II: Summary of evaluation metrics for determining the accuracy of an inferred causal graph.

p

is the number of nodes in the graph. For a window graph with

Q

past lags and

d

time series,

p=(Q+1)d

Benchmark Type	Primary Purpose	Recommended Usage
Simulations	Diagnostic	Investigate the method’s limits, sensitivity to hyperparameters,
		and behaviour relative to a known ground truth
Semi-synthetic	Complexity	Demonstrate performance in a realistic but controlled environment
Real-world	Impact	Prove practical applicability and robustness

TABLE III: Summary of benchmark types, their primary purposes, and recommended usage.

Fig. 3: This diagram demonstrates the representative application domains of TSCD .

Time-Series Causal Discovery

Time-series causal discovery seeks to infer which variables influence others over time and when those effects occur.

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Causal-TS: A Python Library for Causal Discovery in High-Dimensional and Nonstationary Time Series

Mohammad Fesanghary

Bloomberg LP, New York, NY, USA

Time-Series Causal Discovery Causal Discovery Causal Inference Conditional Independence Testing

Open paper AskPDF arXiv

We describe Causal-TS, an open-source Python library for causal discovery in high-dimensional and nonstationary multivariate time series. Causal-TS provides four specialized algorithms-CDNOTS, CDNOTS+, CEDAR, and GRACE-along with wrappers for GES, Granger, LASSO-VAR, and LGES, all sharing a unified conditional independence (CI) test layer with GPU acceleration via PyTorch. A regime discovery pipeline detects structural breaks via pluggable changepoint detectors and runs discovery per regime with regime-specific parameters. A command-line interface, synthetic data generators, and optional DoWhy integration provide an end-to-end pipeline from raw time series to causal effect estimates. The library is pip-installable, tested on Python 3.10--3.12, and available at https://github.com/bloomberg/causal-ts.

Abstract

Time-Series Causal Discovery

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