Deciphering Invariant Feature Decoupling in Source-free Time Series Forecasting with Proxy Denoising

The proliferation of mobile devices generates a massive volume of time series across various domains, where effective time series forecasting enables a variety of real-world applications. This study focuses on a new problem of source-free domain adaptation for time series forecasting. It aims to adapt a pretrained model from sufficient source time series to the sparse target time series domain without access to the source data, embracing data protection regulations. To achieve this, we propose TimePD, the first source-free time series forecasting framework with proxy denoising, where large language models (LLMs) are employed to benefit from their generalization capabilities. Specifically, TimePD consists of three key components: (1) dual-branch invariant disentangled feature learning that enforces representation-and gradient-wise invariance by means of season-trend decomposition; (2) lightweight, parameter-free proxy denoising that dynamically calibrates systematic biases of LLMs; and (3) knowledge distillation that bidirectionally aligns the denoised prediction and the original target prediction. Extensive experiments on real-world datasets offer insight into the effectiveness of the proposed TimePD, outperforming SOT A baselines by 9.3% on average. The widespread deployment of Internet-of-Things (IoT) sensors has produced massive time series data across domains (Sun et al., 2025; Wang et al., 2024a), including traffic (Kieu et al., 2024; Cirstea et al., 2022), weather (Hettige et al., 2024), and energy (Wu et al., 2020). Accurate time series forecasting is crucial, enabling effective decision-making across diverse domains (Liu et al., 2025a; 2024a; Campos et al., 2023). We are seeing impressive advances in machine learning, especially in deep learning, that are successful in effective feature extraction and value creation (Hettige et al., 2024; Liu et al., 2025b).