When GNNs Fail: Quantifying and Overcoming Temporal Correlation Volatility in Time Series
AuthorsChen Shao, Yue Wang, Zhenyi Zhu, Zhanbo Huang, Tobias Käfer, Zonghan Wu, Danai Koutra
This work shows why graph-based time-series models break when correlations shift over time and proposes GLIDE to make them more robust.
Key results
Indicates a highly stable long-term correlation topology.
Indicates an extremely volatile correlation topology.
Maximum synthetic error degradation under topology switching.
Average GLIDE reduction across forecasting horizons 3, 6, and 12.
Average GLIDE reduction across forecasting horizons 3, 6, and 12.
Largest GLIDE improvement on the Exchange Rate benchmark.
What the paper found
This paper shows that graph neural networks for multivariate time-series forecasting can fail when cross-series correlations change rapidly, because static adjacency matrices and even self-attention in Transformers encode the wrong relational structure. It introduces Temporal Correlation Volatility, or TCV, a model-agnostic metric based on the average Frobenius distance between Pearson-correlation graphs inferred from successive sliding windows; Exchange Rate has a near-static TCV of 0.007, while Germany reaches 0.997. In synthetic experiments, Autoformer’s error degradation reaches 36.6% under topology switching, confirming that the problem is representational rather than merely statistical. The proposed GLIDE layer addresses it with path-based message passing, which aggregates higher-order polynomial neighborhoods to reduce noisy direct-edge effects, and Static and Dynamic Propagation Separation, which decomposes persistent correlations from transient, gradient-based shocks. Across 18 baselines and eight benchmarks, including Electricity, Solar, Germany, France, ETTh1, and Exchange Rate, GLIDE remains competitive in static settings and substantially improves dynamic forecasting. On Exchange Rate, its average reductions are 45.6% in RMSE and 78.8% in MAE across horizons 3, 6, and 12, with a maximum MAE reduction of 85.7%. The results position TCV as a practical failure diagnostic and GLIDE as a dynamic-topology inductive bias for time-series GNNs.
Original abstract
Modeling multivariate time series by representing them as graphs, where individual series act as nodes and pairwise temporal corre- lations serve as edges, has gained significant traction. Recent advances in Graph Neural Networks (GNNs) have demonstrated strong perfor- mance by assuming a static graph topology and aggregating information from neighboring series. In this work, we investigate the representa- tional power of GNNs for forecasting under both static and dynamic settings (i.e., when pairwise correlations evolve drastically over time) and identify critical limitations in current architectures. To formalize this, we first propose Temporal Correlation Volatility (TCV), a model- agnostic metric designed to quantify the distributional evolution of these latent structures. We establish a clear connection between TCV and performance degradation, demonstrating that many popular models, including Transformers, generalize poorly in high-TCV settings and are often outperformed by simple structure-agnostic baselines. To address these limitations, we propose Graph Layer for Inference in Dynamic En- vironments (GLIDE), a novel GNN layer enhanced by two theoretically grounded design mechanisms: (D1) Path-based Message Passing, which captures path-based neighborhoods and (D2) Static and Dynamic Propagation Separation, which identifies optimal dynamics via local static approximation. These components significantly improve learning under dynamic topology while preserving robustness in static scenarios. Ex- tensive experiments on synthetic and real-world benchmarks show that GLIDE improves average performance by up to 45.6% across static and dynamic settings, with the largest gain reaching 85.7%. The source code is available at https://github.com/ChenS676/GLIDE.
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