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A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection

Ming Jin, Huan Yee Koh, Qingsong Wen, Daniele Zambon, Cesare Alippi, Geoffrey I. Webb, Irwin King, Shirui Pan

arXiv:2307.03759v3cs.LGcs.AI

TL;DR

Time series analysis needs methods that address complex temporal, spatial, and inter-variable relationships across diverse tasks. This survey synthesizes GNN4TS research through task- and methodology-oriented taxonomies, application reviews, and future directions. It provides a comprehensive account of forecasting, classification, anomaly detection, and imputation research while highlighting GNN4TS applications and open opportunities.

  • Problem

    Time series analysis must handle complex temporal and inter-variable relationships, while existing surveys cover GNN-based methods only within restricted perspectives or domains.

  • Method

    The survey organizes GNN4TS research through task- and methodology-oriented taxonomies, reviews representative studies and applications, and discusses future research directions.

  • Results

    The survey covers four major GNN4TS tasks—forecasting, classification, anomaly detection, and imputation—and provides a unified, fine-grained account of spatial-temporal dependency modeling and model architectures.

  • Takeaways & Limitations

    The survey serves as a resource for practitioners and experts seeking to understand current GNN4TS progress, applications, and research opportunities.

  • Takeaways & Limitations

    Scalability remains challenging for GNNs on vast time-dependent data volumes, particularly when preserving temporal dependencies and enabling efficient inference on resource-constrained edge devices.

Abstract

from arXiv · show

Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis.

1 INTRODUCTION

Time series analytics must address complex temporal and inter-variable relationships across many application domains. This survey reviews GNN-based approaches across major tasks, organizes them through unified taxonomies, examines applications, and identifies future research directions.

  • Time series analytics supports forecasting, classification, anomaly detection, and imputation across fields including transportation, energy, finance, and the Internet-of-Things.
  • Many time series are spatial-temporal, with variables representing locations and localized changes propagating across neighboring regions.
  • GNNs can model inter-variable and inter-temporal relationships in real-world time series through graph-based representations.
  • The survey provides task- and methodology-oriented taxonomies covering problem settings, spatial and temporal dependency modeling, and overall model architecture.
  • It offers a broad, fine-grained, and up-to-date review of GNN4TS without restricting coverage to specific tasks or domains.
  • The survey discusses applications across sectors and proposes potential future research directions for GNN-based time series analysis.

2 DEFINITION AND NOTATION

This section defines time-series representations and their abstraction as spatial-temporal graphs, then introduces GNN message passing and graph-construction strategies. Multivariate series are emphasized because graphs capture both inter-temporal and inter-variable dependencies.

  • Time Series: Time series consist of observations collected over time and may be regularly or irregularly sampled, with univariate and multivariate forms.Irregular sampling is treated as time series data with missing values; multivariate observations are N-dimensional.
  • Spatial-Temporal Graphs: Multivariate time series naturally map to spatial-temporal graphs that characterize dependencies across time steps and variables.Inter-temporal dependencies link time steps within a series, while inter-variable dependencies link different series, such as geographically related sensors.
  • Spatial-Temporal Graphs: A spatial-temporal graph is a sequence of attributed graphs G = {G1, G2, · · · , GT}, with adjacency and feature matrices that may evolve or remain fixed.At time t, Gt = (At, Xt), where At encodes topology and Xt encodes node features.
  • Graph Neural Networks: GNNs learn node representations by aggregating messages from neighboring nodes and combining them with previous node states.The formulation describes spatial GNNs, whose graph convolution exchanges information across neighboring nodes.
  • Graph Construction: GNN-based time-series analysis requires a graph structure, which can be supplied through heuristic construction or learned from data.Heuristics include spatial proximity, pairwise connectivity, pairwise similarity, and functional dependence.
  • Graph Construction: Heuristic graphs encode proximity, connectivity, similarity, or functional dependence using distances, links, cosine similarity, correlation, dynamic time warping, or Granger causality.Functional relations are described as representing or estimating actual node dependencies in the data-generating process.

3 FRAMEWORK AND CATEGORIZATION

The survey organizes GNN-based time series analysis around four tasks and a unified spatial-temporal representation framework. STGNNs encode graph relationships and temporal evolution before task-specific modules perform forecasting, anomaly detection, imputation, or classification.

  • Unified methodological framework: STGNN architectures combine a graph-based processing module with a downstream module specialized for the target time series task.The framework represents these modules as fθ and pϕ, respectively.
  • Task-oriented taxonomy: The task-oriented taxonomy covers forecasting, anomaly detection, imputation, and classification on representations learned by spatial-temporal GNNs.Forecasting may be single-step or multi-step, while anomaly detection commonly uses unsupervised discrepancy modeling.
  • Forecasting: Forecasting predicts future observations from historical graph sequences, using fixed or evolving graph structures and typically squared or absolute forecasting losses.The prediction horizon distinguishes single-step from multi-step forecasting.
  • Anomaly detection: Anomaly detection trains on predominantly normal data and flags anomalous inputs through increased forecast or reconstruction discrepancy, with channel-wise scores supporting diagnosis.Threshold selection should account for anomaly rarity and the desired false alarm rate.
  • Imputation: Imputation estimates missing values through in-sample or out-of-sample formulations, often using synthetic missingness because complete reference series are unavailable during training.The imputation module operates on incomplete input series and is optimized with an imputation loss.
  • Classification: Classification can treat each series as a graph for graph classification or as a node in a dataset graph for node classification.Windowed subsequences may form graph nodes, whereas multiple complete series may provide node features in a dataset-level graph.
  • Methodological framework: The methodological framework categorizes STGNNs by spatial modules, temporal modules, and overall fusion, while the general pipeline preprocesses data, extracts topology, learns representations, and applies task handlers.Spatial modules include spectral, spatial, and hybrid approaches; graph transformers extend message passing methods.

4 GNNS FOR TIME SERIES FORECASTING

GNN forecasting methods explicitly model inter-variable and inter-temporal dependencies through varied spatial, temporal, and fusion designs. The survey organizes them by graph convolution strategy, temporal module, and whether spatial-temporal processing is factorized or coupled.

  • Overview: GNN-based forecasting addresses the spatial correlations that many conventional deep forecasting models leave implicit or overlook.The survey emphasizes explicit modeling of inter-variable and temporal dependencies.
  • Forecasting tasks: Forecasting models are commonly evaluated for multi-step prediction, while a smaller group addresses single-step forecasting.The survey also distinguishes short-term and long-term horizons.
  • Inter-variable dependencies: Spatial dependency methods comprise spectral GNNs, spatial GNNs, and hybrids that model relationships among time series.Spectral methods use graph-signal-processing principles, whereas spatial methods use message passing or diffusion.
  • Taxonomy summary: Table 2 summarizes forecasting methods by task horizon, architecture, temporal domain and module, graph-input requirements, learned relation type, graph heuristics, and missing-value handling.Its notation distinguishes multi-step or single-step and short-term or long-term forecasting.
  • Inter-temporal dependencies: Representative forecasting architectures combine graph operations with recurrent, convolutional, attention-based, or hybrid temporal modules.Temporal dependencies may be modeled in the time domain, frequency domain, or both.
  • Architectural fusion: Spatial-temporal fusion is categorized as discrete factorized, discrete coupled, continuous factorized, or continuous coupled.Factorized designs separate spatial and temporal processing, while coupled designs integrate them into one process; continuous models use neural differential equations.

5 GNNS FOR TIME SERIES ANOMALY DETECTION

The survey frames time series anomaly detection as learning normal behavior and identifying deviations through reconstruction, forecast, or relational discrepancies. GNNs support both detection and diagnosis by modeling dependencies among variables and their changing relationships.

  • Problem formulation: Anomalies are observations or subsequences that deviate from the nominal data-generating process and are difficult to characterize because they are rare.The task includes detecting when anomalies occur and diagnosing their causes.
  • Discrepancy frameworks: Most methods use a backbone-scorer architecture, differing mainly in how the backbone learns nominal structure and how discrepancies are scored.The survey identifies reconstruction, forecast, and relational discrepancy frameworks.
  • Reconstruction discrepancy: Reconstruction frameworks identify anomalies through high reconstruction error, with GNN variants such as MTAD-GAT modeling inter-variable and inter-temporal dependencies.Some methods additionally produce graph-level embeddings for established multivariate detection methods.
  • Forecast discrepancy: Forecast frameworks train GNN forecasters on normal data and score discrepancies between one-step predictions and observed signals.GDN learns graph topology and uses the maximum absolute forecast error across channel variables as its anomaly score.
  • Relational discrepancy: Relational discrepancy frameworks detect shifts in relationships among variables using dynamically learned graph structures.GReLeN scores changes in channel-node in-degree and out-degree, while DyGraphAD predicts evolving graph structures.
  • Hybrid and other discrepancies: Forecast discrepancy methods are described as effective for temporal anomalies, whereas relational discrepancy methods can uncover spatial anomalies hidden in cross-channel relationships.The survey presents hybrid solutions as a way to combine these complementary strengths.

6 GNNS FOR TIME SERIES CLASSIFICATION

GNN-based time series classification models distinguish class-specific patterns and can represent either subsequences within each series or relationships across series samples. Multivariate classification additionally requires modeling inter-variable dependencies.

  • Time series classification assigns categorical labels based on patterns, unlike forecasting or anomaly detection, which target future points or real-time deviations.
  • Series-as-Graph: Series-as-Graph converts each univariate series into a graph whose subsequences are nodes and relationships are edges for GNN-based graph classification.The approach applies a GNN after connecting subsequences according to their relationships.
  • Series-as-Node: Series-as-Node represents each series sample as a node and connects series using relationships that support classification across samples.SimTSC constructs edges from pairwise DTW distances, encodes each series into a feature vector, and classifies the resulting node representations.
  • Series-as-Node: O(L) rather than O(L2) time complexity dramatically reduces computation time for the Series-as-Node approach.
  • Multivariate Time Series Classification: Multivariate classification must capture intricate inter-variable dependencies because analyzing one variable or brain region in isolation may miss comprehensive dynamics.

7 GNNS FOR TIME SERIES IMPUTATION

GNN-based time series imputation addresses missing values by modeling temporal and relational structure, with methods spanning deterministic and probabilistic formulations. Most existing approaches focus on in-sample data, while fewer address unseen series or nodes.

  • Time series imputation estimates missing values, while traditional statistical methods often struggle with complex temporal dependencies and nonlinear relationships.
  • GNN imputation methods are categorized as deterministic, producing one best estimate, or probabilistic, producing a distribution of possible values.
  • Most existing GNN-based methods focus on in-sample imputation, including architectures that interleave graph attention with temporal convolution and deconvolution.GACN models spatiotemporal dependencies in an encoder and maps latent states back to the original feature space.
  • Only a few GNN-based methods address out-of-sample imputation for unobserved time series or new variables.IGNNK uses masked subgraph sampling and signal reconstruction, while INCREASE models heterogeneous spatial and diverse temporal relations.

8 PRACTICAL APPLICATIONS AND RESOURCES

GNNs for time series analysis are applied across transportation, services, energy and environment, physical systems, healthcare, and fraud detection. These applications use graph-based modeling to support prediction, imputation, and system analysis.

  • GNN4TS applications span seven areas: smart transportation, on-demand services, environment and sustainable energy, internet-of-things, physical systems, healthcare, and fraud detection.
  • Smart Transportation: Smart transportation applications include traffic prediction, flight-delay prediction, and traffic-data imputation.Spatiotemporal GNNs support traffic prediction for route planning and congestion management.
  • Environment & Sustainable Energy: Environment and sustainable-energy applications include wind-speed, wind-power, solar-irradiance, and photovoltaic-power prediction.These models capture spatial-temporal dynamics and relationships relevant to energy generation.
  • Physical Systems: Physical-system applications model interacting objects in n-body systems, particle physics, human motion dynamics, and molecular dynamics.Objects are represented as graph nodes, allowing GNNs to model their complex interactions.
  • Other Applications: Other applications extend GNN-based time series analysis to finance, on-demand services, fraud detection, manufacturing, and recommender systems.

9 FUTURE DIRECTIONS

Future GNN4TS research emphasizes pre-training and transfer, robustness, privacy, and scalability. The survey identifies limited data, distribution shifts, privacy exposure, memory constraints, and difficulty preserving temporal dependencies as central challenges.

  • Pre-training, Transfer Learning, and Large Models: Pre-training, transfer learning, and large models may improve GNN4TS when data are sparse or diverse, but large-scale pre-training faces limited data and transferability challenges.
  • Robustness: Robustness research must address perturbations, distribution shifts, noise, and data corruption while developing failure-management strategies.The survey connects these concerns to operational failures in smart-city and healthcare systems.
  • Privacy Enhancing: Privacy protection is challenging because GNNs learn and reconstruct node and edge relationships, while interpretability can expose sensitive information.
  • Scalability: Scalability is constrained by memory demands on vast time-dependent data, and sampling methods may not preserve temporal dependencies.Real-time deployment on edge devices with limited computing power is identified as an important research challenge.

10 CONCLUSIONS

The survey unifies GNN-based time-series research through task- and methodology-oriented taxonomies, covering spatial and temporal dependency modeling, architectures, applications, and future directions.

  • 10 CONCLUSIONS: The survey organizes GNN4TS research across forecasting, classification, anomaly detection, and imputation using task- and methodology-oriented taxonomies.It also examines six application sectors and proposes future research directions.
  • 10 CONCLUSIONS: Methodologically, forecasting models are analyzed through spatial dependency modeling, temporal dependency modeling, and overall architecture.Spatial approaches include spectral, spatial, and hybrid GNNs, while temporal modules include recurrent, convolutional, attention, and hybrid models.
  • 10 CONCLUSIONS: Spectral and hybrid approaches use graph convolutions, localized message passing, attention, multi-graph construction, or neural architecture search to model spatial relations.Examples combine ChebConv with temporal convolution, localized convolutions, or automatically searched GNN instantiations.
  • 10 CONCLUSIONS: Spatial GNN approaches model inter-variable relationships using message passing, graph diffusion, graph transformers, or hypergraphs.Graph transformers provide global receptive fields, while hypergraphs capture dependencies across multiple spatial scales.
  • 10 CONCLUSIONS: Temporal modules model inter-temporal dependencies in the time or frequency domains using recurrent, convolutional, attention-based, and hybrid designs.These designs range from GRU-based models and gated temporal convolutions to self-attention and combinations of GRU with Transformers.

B.2 Discrepancy Frameworks for Anomaly Detection

GNN-based anomaly detection methods commonly use reconstruction, forecasting, or relational discrepancy frameworks, with graph structure learning supporting anomaly scoring and diagnosis.

  • Discrepancy Frameworks: Anomaly detection methods share a backbone-scorer architecture and differ mainly in how the backbone learns nominal structure and how discrepancies are scored.The three framework categories are reconstruction, forecast, and relational discrepancy.
  • Reconstruction Discrepancy: Reconstruction frameworks detect anomalies when an expressive backbone reproduces nominal inputs but fails to reconstruct anomalous inputs outside the learned data manifold.MTAD-GAT uses a variational reconstructor and aggregates channel likelihoods into an anomaly score.
  • Reconstruction Discrepancy: MTAD-GAT employs graph attention to learn inter-variable and inter-temporal dependencies and empirically outperforms LSTM under the same VAE objective.Its attention scores also differ substantially between normal and anomalous periods.
  • Graph Structure: A major limitation is that anomaly-detection GNNs often lack observed graph structures, while fully connected assumptions can introduce noise and weaken normal-structure learning.VGCRN and FuSAGNet address this by learning channel similarities, including a static sparse directed graph with top-k neighbors.
  • Forecast Discrepancy: Forecast frameworks train a GNN for one-step-ahead prediction and flag anomalies through discrepancies between forecasts and actual observations.GST-Pro can predict anomalies at future timestamps without using actual observations in the scoring function.
  • Forecast Discrepancy: GDN learns graph structure and uses graph attention to forecast signals, then exploits learned variable relationships to trace symptomatic anomalies to neighboring root-cause variables.This extends anomaly detection from discrepancy scoring toward automated diagnosis.

APPENDIX C GNNS FOR TIME SERIES CLASSIFICATION

The survey presents GNNs as a distinct perspective for time-series classification, motivated by their ability to represent relationships within and across series samples.

  • APPENDIX C GNNS FOR TIME SERIES CLASSIFICATION: Time-series classification assigns categorical labels from underlying patterns, with earlier approaches centered on distance-based methods and ensembles.Deep learning has been explored to improve performance and scalability, especially with substantial training labels.
  • APPENDIX C GNNS FOR TIME SERIES CLASSIFICATION: GNN classification transforms time-series data into graphs to capture local and global patterns and relationships among samples.This provides a graph-based perspective beyond methods covered by earlier classification surveys.
  • APPENDIX C GNNS FOR TIME SERIES CLASSIFICATION: The survey offers a fresh GNN perspective on both univariate and multivariate time-series classification problems.Its classification treatment includes graph formulations for individual series and datasets of related series.

C.1 Univariate Time Series Classification

For classification, GNNs represent individual series as graphs or nodes, while multivariate settings additionally require modeling inter-variable dependencies and can accommodate irregular sampling.

  • Univariate Time Series Classification: Time-series classification differs from other analyses by identifying patterns that distinguish series samples according to class labels.This contrasts with forecasting future points or detecting real-time anomalies.
  • Series-as-Graph: Series-as-Graph decomposes each univariate series into subsequence nodes connected by relationship edges, then applies a GNN for graph classification.Time2Graph and Time2Graph+ construct shapelet graphs and model relations between shapelets.
  • Series-as-Node: Series-as-Node converts time-series classification into node classification by connecting series samples using relationships such as pairwise DTW distance.SimTSC encodes each series, applies GNN message passing, and classifies the resulting node representations.
  • Series-as-Node: LB-SimTSC reduces DTW preprocessing complexity from O(L2) to O(L) by using the LB Keogh lower bound.The resulting graph retains relationships among series while reducing computation time.
  • Multivariate Time Series Classification: Multivariate classification adds the need to capture intricate inter-variable dependencies across sensor or brain-region series.Spatial-temporal GNNs can be adapted by replacing the forecasting output layer with a classification component.
  • Multivariate Time Series Classification: Raindrop adaptively learns graph structure and interpolates missing observations in embedding space, maintaining robust high-performance classification under irregular sampling.It uses available recorded data to construct a comprehensive representation despite timestamp-specific missing variables.

D.1 In-sample Imputation

In-sample imputation methods estimate missing values within observed time series by modeling spatial-temporal dependencies with graph and temporal components.

  • GACN interleaves graph attention and temporal convolution layers to model spatial-temporal dependencies.Its decoder combines graph attention with temporal deconvolution to map latent states back to the original feature space.

D.2 Out-of-sample Imputation

Out-of-sample imputation remains relatively uncommon, with methods targeting signals from unobserved variables or virtual sensors. Representative approaches use inductive graph learning and real-time kriging.

  • Only a few GNN-based methods address out-of-sample imputation.
  • IGNNK recovers signals for unobserved time series, including new variables or virtual sensors, using masked subgraph sampling and signal reconstruction.
  • Applications: GNN4TS applications span transportation, on-demand services, environment and energy, IoT, physical systems, healthcare, and fraud detection.

APPENDIX F DATASETS AND IMPLEMENTATIONS

The appendix surveys benchmark datasets and open-source implementations across time-series tasks, while highlighting evaluation gaps and future research challenges. It emphasizes the need for representative data, realistic metrics, robustness, interpretability, uncertainty quantification, and scalable GNNs.

  • Tables 6 and 7 summarize selected benchmark datasets and open-source implementations of representative approaches.
  • Forecasting and Imputation Benchmarks: Traffic benchmarks include METR-LA, PEMS-BAY, PeMS variants, Xiamen, Beijing, NYC-Taxi, NYC-Bike, AQI, and AQI-36.These datasets cover sensors, traffic measurements, pollutant concentrations, taxi trips, bike trajectories, and air-quality indices.
  • Anomaly Detection Benchmarks: Anomaly-detection research relies heavily on SMD, MSL, SMAP, SWAT, and WADI, whose representativeness has been critically questioned.The survey calls for more diverse datasets and fair benchmarking against baseline models.
  • Future Directions: Emerging directions include pre-training and transfer learning, alongside unresolved challenges in data availability and capturing spatial-temporal dependencies.
  • Future Directions: Future GNN4TS systems must address robustness, interpretability, uncertainty quantification, and the memory demands of large graphs.The survey links robustness to perturbations and distribution shifts, notes that many models provide point estimates, and identifies full adjacency and embedding computation as memory-intensive.
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