Source-free domain adaptation (SFDA) aims to adapt a pretrained model from a labeled source domain to an unlabeled target domain without access to the source domain data, preserving source domain privacy. Despite its prevalence in visual applications, SFDA is largely unexplored in time series applications. The existing SFDA methods that are mainly designed for visual applications may fail to handle the temporal dynamics in time series, leading to impaired adaptation performance. To address this challenge, this paper presents a simple yet effective approach for source-free domain adaptation on time series data, namely MAsk and imPUte (MAPU). First, to capture temporal information of the source domain, our method performs random masking on the time series signals while leveraging a novel temporal imputer to recover the original signal from a masked version in the embedding space. Second, in the adaptation step, the imputer network is leveraged to guide the target model to produce target features that are temporally consistent with the source features. To this end, our MAPU can explicitly account for temporal dependency during the adaptation while avoiding the imputation in the noisy input space. Our method is the first to handle temporal consistency in SFDA for time series data and can be seamlessly equipped with other existing SFDA methods. Extensive experiments conducted on three real-world time series datasets demonstrate that our MAPU achieves significant performance gain over existing methods. Our code is available at \url{https://github.com/mohamedr002/MAPU_SFDA_TS}.
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