When Forecasting Fails: Overcoming Temporal Correlation Shift in Time Series

Graph Neural Networks (GNNs) for multivariate time series forecasting typically assume a static graph topology, despite real-world dependencies evolving over time. In this work, we study the representational limitations of existing graph-based forecasting architectures under dynamic topology and theoretically characterize how structural variation degrades their ability to model evolving inter-series dependencies. Motivated by these findings, we propose Graph Layer for Inference in Dynamic Environments (GLIDE), a lightweight GNN layer with two key mechanisms: (D1) Path-based Message Passing, which captures stable higher-order interactions through path-based aggregation, and (D2) Static and Dynamic Propagation Separation, which separates persistent topology from transient structural dynamics. Experiments on synthetic and real-world benchmarks show that GLIDE consistently outperforms state-of-the-art baselines, achieving up to 85.7% improvement. Code: \url{https://anonymous.4open.science/r/GLIDE-7E26/}.