PAMod: Modeling Cyclical Shifts via Phase-Amplitude Modulation for Non-stationary Time Series Forecasting

arXiv cs.AI / 5/4/2026

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Key Points

The paper proposes PAMod, a lightweight framework for forecasting non-stationary time series where mean and variance shift over time in cyclical ways.
PAMod models distribution shifts in a normalized feature space using phase-amplitude modulation: phase modulation targets mean (location) shifts and amplitude modulation targets variance (scale) changes.
The authors mathematically prove that modulation in the normalized space is equivalent to dynamic denormalization, unifying distribution adaptation with representation learning.
Experiments across twelve real-world benchmarks show PAMod achieves state-of-the-art accuracy while using fewer computational resources.
PAMod is presented as a plug-and-play mechanism that can be integrated with existing time-series forecasting methods to improve their performance.

Abstract

Real-world time series forecasting faces the fundamental challenge of non-stationary statistical properties, including shifts in mean and variance over time. While reversible instance normalization (RevIN) has shown promise by stationarizing inputs and denormalizing outputs, it relies on the strong assumption that historical and future distributions remain identical. We observe that in many practical applications, distribution shifts follow cyclical patterns that correlate with periodic positions (e.g., seasonal and holiday volatility). To this end, we propose PAMod, a lightweight yet powerful framework that models cyclical distribution shifts via Phase-Amplitude Modulation in the normalized feature space. PAMod learns periodic embeddings to modulate representations: phase modulation captures mean shifts, while amplitude modulation adapts to variance changes. Crucially, we prove mathematically that modulating in normalized space is equivalent to applying dynamic denormalization, offering an elegant unification of distribution adaptation and representation learning. Extensive experiments on twelve real-world benchmarks demonstrate that PAMod achieves state-of-the-art performance with fewer computational resources. Furthermore, our modulation mechanism, as a novel plug-and-play technique, can improve existing time-series forecasting methods with simple integration.