PhaseAlign: Stage-Dependent Phase Modeling For Long-Term Time Series Forecasting

Long-term time series forecasting relies on recurrent structure, but identifying periodic patterns alone does not indicate where they will reappear in the future. Phase provides this temporal reference, motivating different explicit uses for historical modeling and future generation. Historical modeling relies on relative phase relations among positions in the observed window, whereas future generation preserves the phase reference of the observed window to determine where recurrent structure will appear next. Motivated by this distinction, we propose PhaseAlign, which extracts a shared complex-spectrum representation from the observed window and uses its phase information differently for historical modeling and future generation. For historical modeling, dominant frequencies are used to construct relative harmonic relations that guide attention over the observed sequence. For future generation, the corresponding window-referenced phase states are propagated to future positions along the forecast horizon, providing phase-aware conditioning for future queries. Experiments on seven standard long-term forecasting benchmarks demonstrate strong forecasting performance, while ablation results show consistent advantages of stage-dependent over unified phase modeling. Code is available at this repository: https://github.com/Time358/PhaseAlign-main