  Source-free domain adaptation (SFDA) aims to adapt a model pre-trained on a
labeled source domain to an unlabeled target domain without access to source
data, preserving the source domain's privacy. While SFDA is prevalent in
computer vision, it remains largely unexplored in time series analysis.
Existing SFDA methods, designed for visual data, struggle to capture the
inherent temporal dynamics of time series, hindering adaptation performance.
This paper proposes MAsk And imPUte (MAPU), a novel and effective approach for
time series SFDA. MAPU addresses the critical challenge of temporal consistency
by introducing a novel temporal imputation task. This task involves randomly
masking time series signals and leveraging a dedicated temporal imputer to
recover the original signal within the learned embedding space, bypassing the
complexities of noisy raw data. Notably, MAPU is the first method to explicitly
address temporal consistency in the context of time series SFDA. Additionally,
it offers seamless integration with existing SFDA methods, providing greater
flexibility. We further introduce E-MAPU, which incorporates evidential
uncertainty estimation to address the overconfidence issue inherent in softmax
predictions. To achieve that, we leverage evidential deep learning to obtain a
better-calibrated pre-trained model and adapt the target encoder to map
out-of-support target samples to a new feature representation closer to the
source domain's support. This fosters better alignment, ultimately enhancing
adaptation performance. Extensive experiments on five real-world time series
datasets demonstrate that both MAPU and E-MAPU achieve significant performance
gains compared to existing methods. These results highlight the effectiveness
of our proposed approaches for tackling various time series domain adaptation
problems.
