The transfer of models trained on labeled datasets in a source domain to unlabeled target domains is made possible by unsupervised domain adaptation (UDA). However, when dealing with complex time series models, the transferability becomes challenging due to the dynamic temporal structure that varies between domains, resulting in feature shifts and gaps in the time and frequency representations. Furthermore, tasks in the source and target domains can have vastly different label distributions, making it difficult for UDA to mitigate label shifts and recognize labels that only exist in the target domain. We present RAINCOAT, the first model for both closed-set and universal DA on complex time series. RAINCOAT addresses feature and label shifts by considering both temporal and frequency features, aligning them across domains, and correcting for misalignments to facilitate the detection of private labels. Additionally,RAINCOAT improves transferability by identifying label shifts in target domains. Our experiments with 5 datasets and 13 state-of-the-art UDA methods demonstrate that RAINCOAT can achieve an improvement in performance of up to 16.33%, and can effectively handle both closed-set and universal adaptation.