TimeAPN: Adaptive Amplitude-Phase Non-Stationarity Normalization for Time Series Forecasting

Non-stationarity is a fundamental challenge in multivariate long-term time series forecasting, often manifested as rapid changes in amplitude and phase. These variations lead to severe distribution shifts and consequently degrade predictive performance. Existing normalization-based methods primarily rely on first- and second-order statistics, implicitly assuming that distributions evolve smoothly and overlooking fine-grained temporal dynamics. To address these limitations, we propose TimeAPN, an Adaptive Amplitude-Phase Non-Stationarity Normalization framework that explicitly models and predicts non-stationary factors from both the time and frequency domains. Specifically, TimeAPN first models the mean sequence jointly in the time and frequency domains, and then forecasts its evolution over future horizons. Meanwhile, phase information is extracted in the frequency domain, and the phase discrepancy between the predicted and ground-truth future sequences is explicitly modeled to capture temporal misalignment. Furthermore, TimeAPN incorporates amplitude information into an adaptive normalization mechanism, enabling the model to effectively account for abrupt fluctuations in signal energy. The predicted non-stationary factors are subsequently integrated with the backbone forecasting outputs through a collaborative de-normalization process to reconstruct the final non-stationary time series. The proposed framework is model-agnostic and can be seamlessly integrated with various forecasting backbones. Extensive experiments on seven real-world multivariate datasets demonstrate that TimeAPN consistently improves long-term forecasting accuracy across multiple prediction horizons and outperforms state-of-the-art reversible normalization methods.