arXiv:2605.00466cs.LGcs.AI2026-05

用相位-振幅调制建模周期性分布变化,提升非平稳时间序列预测精度

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

论文配图:PAMod: Modeling Cyclical Shifts via Phase-Amplitude Modulation for Non-stationary Time Series Forecasting
图 1 · 摘自论文原文
  • 在归一化空间中通过相位调制均值、振幅调制方差,捕捉周期性分布偏移
  • 在12个真实数据集上达到当前最佳性能,计算开销更低
  • 可作为通用模块插入现有模型,无需复杂改造

现实世界的时间序列预测面临非平稳统计特性(如均值和方差随时间变化)的根本挑战。尽管可逆实例归一化(RevIN)通过归一化输入并反归一化输出展现潜力,但其依赖历史与未来分布相同的强假设。我们观察到,在许多实际场景中,分布偏移呈现与周期位置相关的周期性模式(如季节性和节假日波动)。为此,我们提出PAMod,一种轻量且高效的方法,通过在归一化特征空间中的相位-振幅调制来建模周期性分布偏移。PAMod学习周期嵌入以调制表示:相位调制捕捉均值偏移,振幅调制适应方差变化。关键的是,我们从数学上证明了在归一化空间中调制等价于动态反归一化,实现了分布适应与表征学习的优雅统一。在12个真实世界基准上的广泛实验表明,PAMod以更少计算资源实现最先进性能。此外,该调制机制作为一种新型即插即用技术,可简单集成至现有时序预测方法中,显著提升效果。

原文摘要 · Abstract (English)

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.

时间序列非平稳周期建模归一化

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