APT: Affine Prototype-Timestamp For Time Series Forecasting Under Distribution Shift

TL;DR

This paper introduces APT, a lightweight module that enhances time series forecasting models by incorporating global distribution features, significantly improving performance under distribution shift without adding much computational cost.

Contribution

The paper proposes APT, a novel plug-in for time series forecasting that dynamically generates affine parameters using timestamp-conditioned prototypes, addressing distribution shift issues.

Findings

APT improves forecasting accuracy under distribution shift.

APT is compatible with various backbones and normalization methods.

Extensive experiments validate APT's effectiveness across datasets.

Abstract

Time series forecasting under distribution shift remains challenging, as existing deep learning models often rely on local statistical normalization (e.g., mean and variance) that fails to capture global distribution shift. Methods like RevIN and its variants attempt to decouple distribution and pattern but still struggle with missing values, noisy observations, and invalid channel-wise affine transformation. To address these limitations, we propose Affine Prototype Timestamp (APT), a lightweight and flexible plug-in module that injects global distribution features into the normalization-forecasting pipeline. By leveraging timestamp conditioned prototype learning, APT dynamically generates affine parameters that modulate both input and output series, enabling the backbone to learn from self-supervised, distribution-aware clustered instances. APT is compatible with arbitrary forecasting backbones and normalization strategies while introducing minimal computational overhead. Extensive experiments across six benchmark datasets and multiple backbone-normalization combinations demonstrate that APT significantly improves forecasting performance under distribution shift.