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

Fuente: arXiv
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Main Authors: Zhou, Yingbo, Ye, Yutong, Li, Shuhao, Qian, Rui, Huang, Qiang, Liu, Lemao, Sun, Li, Dou, Dejing
Format: Preprint
Published: 2026
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author Zhou, Yingbo
Ye, Yutong
Li, Shuhao
Qian, Rui
Huang, Qiang
Liu, Lemao
Sun, Li
Dou, Dejing
author_facet Zhou, Yingbo
Ye, Yutong
Li, Shuhao
Qian, Rui
Huang, Qiang
Liu, Lemao
Sun, Li
Dou, Dejing
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_00466
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle PAMod: Modeling Cyclical Shifts via Phase-Amplitude Modulation for Non-stationary Time Series Forecasting
Zhou, Yingbo
Ye, Yutong
Li, Shuhao
Qian, Rui
Huang, Qiang
Liu, Lemao
Sun, Li
Dou, Dejing
Machine Learning
Artificial Intelligence
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.
title PAMod: Modeling Cyclical Shifts via Phase-Amplitude Modulation for Non-stationary Time Series Forecasting
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2605.00466