Improving Graph Models for Time Series

Summary & Methodology Analysis

Graph Neural Networks (GNNs) often struggle in multivariate time series forecasting when the underlying graph topology is unstable. The authors introduce the Temporal Correlation Volatility (TCV) metric to quantify how these latent graph structures evolve over time. To address performance degradation in dynamic settings, they propose the Graph Layer for Inference in Dynamic Environments (GLIDE). This architecture uses a path-based message passing mechanism that utilizes K-th order polynomial reachability to capture stable higher-order interactions among nodes, effectively filtering out noise from rapidly changing temporal correlations. The architecture also employs a separation strategy that decomposes adjacency matrices into persistent static components and transient dynamic components using kernel-weighted estimation to handle time-varying topology. Finally, a 1D convolutional projection maps these refined representations to future time steps. Through extensive testing against 18 baselines, the model demonstrates significant performance stability compared to popular approaches like Transformers, which can suffer up to 36.6 percent degradation in high-TCV scenarios. The authors validated these results on eight benchmarks, including ETTh1, Exchange Rate, and energy datasets from Germany and France. Despite these gains, the current approach has limitations. The theoretical framework relies on an assumption of mutually independent temporal perturbations for analytical tractability, which may not hold in real-world energy or finance domains where dependencies are prevalent. Additionally, because TCV currently relies on Pearson correlation, the method is limited to capturing linear relationships between variables.