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 SOTA baselines by 9.3% on average.