FIRE: Fourier-Informed Regime Adaptive Estimation for Non-Stationary Time Series Forecasting

Non-stationarity remains a critical challenge in multivariate time series forecasting because data distributions and temporal dependencies continuously evolve over time. Recent frequency-domain models have demonstrated the value of spectral representations, yet most of them jointly model amplitude and phase within unified complex embeddings, overlooking their distinct physical roles and evolutionary behaviors. From a signal processing perspective, amplitude characterizes the strength of frequency components, whereas phase encodes their temporal alignment. These distinct physical roles and transformation properties motivate dedicated modeling of amplitude and phase under non-stationarity. We propose FIRE (Fourier Informed Regime Adaptive Estimation), a forecasting framework that explicitly decouples amplitude and phase into dedicated learning branches. To adapt these branches to evolving dynamics, FIRE introduces a signal-informed modulation mechanism driven by two historical window statistics: the Amplitude Non-stationarity Index (ANI) and the Phase Irregularity Index (PII). Across 12 diverse real-world benchmarks, FIRE achieves state-of-the-art forecasting performance against competitive baselines, securing the lowest average MSE and MAE on 9 and 10 datasets, respectively. Controlled ablations demonstrate the benefits of amplitude-phase decoupling and ANI/PII guided adaptive modulation, while channel-level analyses show larger forecasting gains for the evaluated channels with higher ANI and PII.