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

2026-03-18

AI Summary

Multivariate long-term time series forecasting is often hindered by non-stationarity induced by rapid changes in amplitude and phase, leading to distribution shifts and degraded performance. To address this, this work proposes TimeAPN, a novel framework that jointly models the evolution of mean sequences in the time–frequency domain and explicitly captures phase discrepancies and amplitude fluctuations. TimeAPN introduces an adaptive normalization scheme coupled with a model-agnostic co-de-normalization mechanism, thereby relaxing the conventional reliance on low-order statistical assumptions of stationarity. Extensive experiments demonstrate that TimeAPN significantly outperforms existing reversible normalization methods across seven real-world multivariate datasets, consistently improving long-term forecasting accuracy under various prediction horizons.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Activity and Plan Recognition
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• non-stationarity
• time series forecasting
• amplitude-phase variation
• distribution shift
• multivariate time series

Innovation

• Amplitude-Phase Modeling
• Non-Stationarity Normalization
• Frequency-Time Domain Fusion
• Adaptive Normalization
• Long-term Time Series Forecasting