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ForecastGrapher: Redefining Multivariate Time Series Forecasting with Graph Neural Networks

Wanlin Cai, Kun Wang, Hao Wu, Xiaoxu Chen, Yuankai Wu

TL;DR

ForecastGrapher reframes multivariate time series forecasting as node regression on a graph, treating each variate as a node with temporal embeddings and a layer-wise self-learnable adjacency A^l to capture inter-series correlations. Its core novelty, the Group Feature Convolution GNN (GFC-GNN), diversifies node feature distributions by partitioning embeddings into G groups and applying kernel-length varied 1D convolutions, followed by a residual fusion to produce forecasts. Across twelve benchmarks, ForecastGrapher achieves state-of-the-art results, notably on high-dimensional datasets like Electricity and PEMS, and ablation studies validate the importance of variate embeddings, adaptive graphs, and the GFC mechanism. The work offers a flexible, end-to-end framework that extends GNNs’ expressive power for long-horizon MVTS forecasting and provides a foundation for broader time-series analysis tasks with interpretable inter-series relationships.

Abstract

The challenge of effectively learning inter-series correlations for multivariate time series forecasting remains a substantial and unresolved problem. Traditional deep learning models, which are largely dependent on the Transformer paradigm for modeling long sequences, often fail to integrate information from multiple time series into a coherent and universally applicable model. To bridge this gap, our paper presents ForecastGrapher, a framework reconceptualizes multivariate time series forecasting as a node regression task, providing a unique avenue for capturing the intricate temporal dynamics and inter-series correlations. Our approach is underpinned by three pivotal steps: firstly, generating custom node embeddings to reflect the temporal variations within each series; secondly, constructing an adaptive adjacency matrix to encode the inter-series correlations; and thirdly, augmenting the GNNs' expressive power by diversifying the node feature distribution. To enhance this expressive power, we introduce the Group Feature Convolution GNN (GFC-GNN). This model employs a learnable scaler to segment node features into multiple groups and applies one-dimensional convolutions with different kernel lengths to each group prior to the aggregation phase. Consequently, the GFC-GNN method enriches the diversity of node feature distribution in a fully end-to-end fashion. Through extensive experiments and ablation studies, we show that ForecastGrapher surpasses strong baselines and leading published techniques in the domain of multivariate time series forecasting.

ForecastGrapher: Redefining Multivariate Time Series Forecasting with Graph Neural Networks

TL;DR

ForecastGrapher reframes multivariate time series forecasting as node regression on a graph, treating each variate as a node with temporal embeddings and a layer-wise self-learnable adjacency A^l to capture inter-series correlations. Its core novelty, the Group Feature Convolution GNN (GFC-GNN), diversifies node feature distributions by partitioning embeddings into G groups and applying kernel-length varied 1D convolutions, followed by a residual fusion to produce forecasts. Across twelve benchmarks, ForecastGrapher achieves state-of-the-art results, notably on high-dimensional datasets like Electricity and PEMS, and ablation studies validate the importance of variate embeddings, adaptive graphs, and the GFC mechanism. The work offers a flexible, end-to-end framework that extends GNNs’ expressive power for long-horizon MVTS forecasting and provides a foundation for broader time-series analysis tasks with interpretable inter-series relationships.

Abstract

The challenge of effectively learning inter-series correlations for multivariate time series forecasting remains a substantial and unresolved problem. Traditional deep learning models, which are largely dependent on the Transformer paradigm for modeling long sequences, often fail to integrate information from multiple time series into a coherent and universally applicable model. To bridge this gap, our paper presents ForecastGrapher, a framework reconceptualizes multivariate time series forecasting as a node regression task, providing a unique avenue for capturing the intricate temporal dynamics and inter-series correlations. Our approach is underpinned by three pivotal steps: firstly, generating custom node embeddings to reflect the temporal variations within each series; secondly, constructing an adaptive adjacency matrix to encode the inter-series correlations; and thirdly, augmenting the GNNs' expressive power by diversifying the node feature distribution. To enhance this expressive power, we introduce the Group Feature Convolution GNN (GFC-GNN). This model employs a learnable scaler to segment node features into multiple groups and applies one-dimensional convolutions with different kernel lengths to each group prior to the aggregation phase. Consequently, the GFC-GNN method enriches the diversity of node feature distribution in a fully end-to-end fashion. Through extensive experiments and ablation studies, we show that ForecastGrapher surpasses strong baselines and leading published techniques in the domain of multivariate time series forecasting.
Paper Structure (33 sections, 1 theorem, 10 equations, 11 figures, 9 tables)

This paper contains 33 sections, 1 theorem, 10 equations, 11 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Backbone Networks Used in Time Series Forecasting
  4. Graph Neural Networks
  5. Methodology
  6. Problem Formulation
  7. Embedding the Time Series
  8. Graph Neural Networks
  9. Self-Learnable Adjacency Matrix
  10. Learnable Scaler and Group Feature Convolution
  11. Combining Groups and Generating Forecast Results
  12. Experiments
  13. Experimental Setup
  14. Datasets
  15. Baselines
  16. ...and 18 more sections

Key Result

Theorem 1

Given a graph $\mathcal{G}(\mathcal{V}, \mathcal{E})$, we denote the nodes belonging to class $C_i$ as $\{v_i \mid v_i \in C_i\}$. Assume the feature distribution $\mathbf{h}_{i}$ of nodes in $C_i$ follows an i.i.d. Gaussian distribution $\mathcal{N}(\mu_i, \sigma_i^2)$. For any two distinct classes

Figures (11)

  • Figure 1: In ForecastGrapher, each variate is treated as a node within a graph, transforming the multivariate time series forecasting problem into a node regression task.
  • Figure 2: The overall structure of ForecastGrapher is designed to address a node regression task. The model considers each time series as a node and generates a corresponding node embedding. Next, it employs learnable scalers to partition the node embedding into multiple groups. Subsequently, several layers of GFC-GNN are stacked (the red color indicates the dimension to which the corresponding neural networks are applied). Finally, ForecastGrapher utilizes node projection for forecasting.
  • Figure 3: The GFC mechanism enhances the diversity of node embedding distributions: Convoluting the node feature with two distinct kernel lengths results in two distinct distributions.
  • Figure 4: Visualization of input 96 and output 96 prediction results on the Electricity dataset.
  • Figure 5: Analysis of the model robustness and efficiency.
  • ...and 6 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof