Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting

TLDR

Multivariate time‑series forecasting is essential in many applications, yet it is difficult because it must capture both intra‑series temporal correlations and inter‑series relationships, and existing methods typically model only temporal dependencies while relying on pre‑defined priors for inter‑series links. This work introduces the Spectral Temporal Graph Neural Network (StemGNN) to enhance forecasting accuracy by jointly modeling these correlations. StemGNN integrates Graph Fourier Transform for inter‑series dependencies and Discrete Fourier Transform for temporal dynamics, then applies convolutional and sequential modules to learn clear spectral patterns in an end‑to‑end framework. StemGNN automatically learns inter‑series correlations from data and demonstrates improved forecasting performance across ten real‑world datasets. Code is available at https://github.com/microsoft/StemGNN/.

Abstract

Multivariate time-series forecasting plays a crucial role in many real-world applications. It is a challenging problem as one needs to consider both intra-series temporal correlations and inter-series correlations simultaneously. Recently, there have been multiple works trying to capture both correlations, but most, if not all of them only capture temporal correlations in the time domain and resort to pre-defined priors as inter-series relationships. In this paper, we propose Spectral Temporal Graph Neural Network (StemGNN) to further improve the accuracy of multivariate time-series forecasting. StemGNN captures inter-series correlations and temporal dependencies \textit{jointly} in the \textit{spectral domain}. It combines Graph Fourier Transform (GFT) which models inter-series correlations and Discrete Fourier Transform (DFT) which models temporal dependencies in an end-to-end framework. After passing through GFT and DFT, the spectral representations hold clear patterns and can be predicted effectively by convolution and sequential learning modules. Moreover, StemGNN learns inter-series correlations automatically from the data without using pre-defined priors. We conduct extensive experiments on ten real-world datasets to demonstrate the effectiveness of StemGNN. Code is available at https://github.com/microsoft/StemGNN/.