SEED: Spectral Entropy-Guided Evaluation of SpatialTemporal Dependencies for Multivariate Time Series Forecasting

Feng Xiong; Zongxia Xie; Yanru Sun; Haoyu Wang; Jianhong Lin

Paper

SEED: Spectral Entropy-Guided Evaluation of SpatialTemporal Dependencies for Multivariate Time Series Forecasting

Abstract

Effective multivariate time series forecasting often benefits from accurately modeling complex inter-variable dependencies. However, existing attention- or graph-based methods face three key issues: (a) strong temporal self-dependencies are often disrupted by irrelevant variables; (b) softmax normalization ignores and reverses negative correlations; (c) variables struggle to perceive their temporal positions. To address these, we propose \textbf{SEED}, a Spectral Entropy-guided Evaluation framework for spatial-temporal Dependency modeling. SEED introduces a Dependency Evaluator, a key innovation that leverages spectral entropy to dynamically provide a preliminary evaluation of the spatial and temporal dependencies of each variable, enabling the model to adaptively balance Channel Independence (CI) and Channel Dependence (CD) strategies. To account for temporal regularities originating from the influence of other variables rather than intrinsic dynamics, we propose Spectral Entropy-based Fuser to further refine the evaluated dependency weights, effectively separating this part. Moreover, to preserve negative correlations, we introduce a Signed Graph Constructor that enables signed edge weights, overcoming the limitations of softmax. Finally, to help variables perceive their temporal positions and thereby construct more comprehensive spatial features, we introduce the Context Spatial Extractor, which leverages local contextual windows to extract spatial features. Extensive experiments on 12 real-world datasets from various application domains demonstrate that SEED achieves state-of-the-art performance, validating its effectiveness and generality.