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

TL;DR

PAMod is a novel framework that models cyclical distribution shifts in non-stationary time series using phase-amplitude modulation, improving forecasting accuracy and efficiency.

Contribution

It introduces a lightweight, plug-and-play modulation technique that captures cyclical shifts via phase and amplitude modulation in normalized space.

Findings

PAMod achieves state-of-the-art results on twelve real-world benchmarks.

The modulation mechanism can enhance existing forecasting models with simple integration.

PAMod requires fewer computational resources than previous methods.

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.