Homomorphic-Controlled Augmentation for Time Series Forecasting

Abstract

Data augmentation is an effective strategy to improve sample efficiency and reduce overfitting in time series forecasting. However, common data augmentation techniques act locally, limiting their influence on global characteristics and potentially distorting the overall temporal structure of one-dimensional time series. Recent approaches manipulate spectral components to augment time series, and their perturbations tend to be coarse and stochastic, which may lead to un-realistic samples. In this paper, we propose Homomorphic-Controlled Augmentation (HCA), a framework that leverages homomorphic decomposition to disentangle a time series into three interpretable components—the phase spectrum, spectral envelope, and harmonic details. Each component can then be independently manipulated to enable targeted augmentation that preserves temporal structure while simulating realistic variations. Extensive evaluation on six real-world datasets demonstrates that HCA consistently outperforms base models without augmentation as well as state-of-the-art augmentation methods, producing more accurate and stable predictions.