Recently, deep learning has received increasing attention from researchers due to its excellent performance in various scenarios, but these methods often rely on the independent and identically distribution assumption. Domain adaptation is a problem proposed to mitigate the impact of distribution offset, which uses labeled source domain data and unlabeled target domain data to achieve better performance on target data. Existing methods are devised for static data, while the methods for time series data need to capture the dependencies between variables. Although these methods use feature extractors for time series data, such as recurrent neural networks, to learn the dependencies between variables, they often extract redundant information. This information is easily entangled with semantic information, affecting the model performance. To solve these problems, this study proposes a path-signature-based time-series domain adaptation (PSDA). On the one hand, this method uses path signature transformation to capture sparse dependencies between variables and eliminate redundant correlations while preserving semantic dependencies, thereby facilitating the extraction of discriminative features from temporal data. On the other hand, the invariant dependency relationships are preserved by constraining the consistency of dependency relationships among different domains, and the changing dependency relationships between domains are excluded, which is conducive to extracting generalized features from temporal data. Based on the above methods, the study further proposes a distance metric and generalized boundary theory and obtains the best experimental results on multiple time series domain adaptation standard datasets.