Adaptive Phase Alignment: Correcting Phase Drift in Multivariate Time Series Forecasting

Phase drift is pervasive in real-world periodic time series, causing historical periodic structures to become misaligned with future observations and degrading multivariate forecasting performance. Existing methods for modeling periodic patterns often adopt fixed phase assignments within each cycle or establish correspondence using a shared set of phase indices. Such representations do not characterize frequency-specific phase variations or adapt periodic correspondence to their changes across observation windows, and may consequently preserve unreliable temporal information corrupted by phase drift and noise. To address these limitations, we characterize phase drift through the window-dependent variation of phase offsets across individual frequency components, providing a basis for adapting periodic representations to changing phase structures. Building on this formulation, we propose Adaptive Phase Alignment (APA), a lightweight and plug-and-play module for correcting phase drift. APA decomposes each variate into frequency components and applies a compact complex-valued affine mapping whose relative phase response depends on the current spectral state, allowing shared parameters to induce component- and window-dependent phase variations. It then converts these variations into representation-level phase alignment through temporal gating, which adaptively reweights periodic information across temporal positions. The resulting representation enhances reliable periodic cues while attenuating information corrupted by phase drift and noise. Extensive experiments on nine real-world benchmarks demonstrate state-of-the-art forecasting performance and consistent improvements across diverse forecasting backbones. Notably, APA achieves strong performance even with a shallow MLP backbone while introducing low computational overhead.