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

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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

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.
PrincipleExample Method(s)Graph TypeDynamicsCausal Sufficiency
Granger causalityLinear Granger Causality (GC) [ 1 ]SummaryStochasticAssumed
Granger causalityNeural GC [ 9 ]SummaryStochasticAssumed
Information-theoreticTransfer entropy [ 10 ]SummaryStochasticAssumed
Cross mappingCCM [ 6 ]SummaryDeterministicRelaxed
Constraint-basedPCMCI [ 11 ]WindowStochasticAssumed
Constraint-basedLPCMCI [ 12 ]WindowStochasticRelaxed
TABLE I: Some representative TSCD methods from each inference principle and a comparison of their key assumptions.
MetricRangeTargetIntuition
Precision[0,1][0,1]↑\uparrowAvoiding false causal links
Recall[0,1][0,1]↑\uparrowDetecting existing causal links
F1[0,1][0,1]↑\uparrowRecall-Precision balance
SHD[0,p2][0,p^{2}]↓\downarrowNumber of structural errors
SID[0,p(p−1)][0,p(p-1)]↓\downarrowNumber of causal effect errors
TABLE II: Summary of evaluation metrics for determining the accuracy of an inferred causal graph. pp is the number of nodes in the graph. For a window graph with QQ past lags and dd time series, p=(Q+1)dp=(Q+1)d .
Benchmark TypePrimary PurposeRecommended Usage
SimulationsDiagnosticInvestigate the method’s limits, sensitivity to hyperparameters,
  and behaviour relative to a known ground truth
Semi-syntheticComplexityDemonstrate performance in a realistic but controlled environment
Real-worldImpactProve 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 .
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