CAST-Norm: Coupled Adaptive Spatio-Temporal Normalization for Multivariate Time Series Forecasting

Distribution shift fundamentally hinders the efficacy of deep models in Multivariate Time Series Forecasting (MTSF). While mitigating non-stationarity requires characterizing both intra- and inter-series shifts, existing literature is predominantly constrained by a limiting ''Decoupled View'', erroneously treating them as orthogonal components. Specifically, proxy-based methods exhibit a ''Spatial Stationarity Bias,'' while proxy-free methods reinforce decoupling via disjoint modules. We theoretically prove that these shifts are mutually coupled; consequently, addressing them in isolation neglects their inherent interaction. To bridge this gap, we propose Coupled Adaptive Spatio-Temporal Normalization (CAST-Norm). Technically, CAST-Norm employs a Hybrid Inter-Intra Series Normalization strategy to isolate systematic shifts and yield spatiotemporally stationary patterns. Furthermore, to overcome the ''Fallacy of Independent Restoration,'' we design a Coupled Adaptive Denormalization mechanism. Instead of reversing statistics independently, it leverages learned spatiotemporal dependencies to jointly modulate the restoration process, ensuring the recovered distribution accurately reflects the non-stationary future. Extensive experiments on eight real-world datasets across four backbone architectures demonstrate that CAST-Norm consistently outperforms state-of-the-art methods. Code is available at https://github.com/xhhmacau/CAST_Norm.