With the rapid development of Internet of Things (IoT) technology, a large amount of time series data generated by smart devices plays a vital role in anomaly detection tasks. However, existing methods mainly focus on abnormal patterns in the time dimension, while ignoring the spatial correlation between variables, which limits the ability to identify complex abnormal patterns. To this end, this paper proposes a spatiotemporal anomaly detection model (Self-Attentive Temporal Anomaly Detection, SATAD) based on the self-attention mechanism to simultaneously learn temporal normality and spatial normality. Specifically, SATAD contains three key modules: Temporal Anomaly Modeling (TAM), Spatial Anomaly Modeling (SAM), and Self-Attentive Fusion (SAF). TAM models temporal dependency by learning the ordering rules of subsequences, while SAM learns spatial normality by modeling the distribution pattern of time series in the representation space. In addition, SAF further optimizes the fusion of temporal-spatial features to enhance the generalization ability of the model. Experimental results show that SATAD outperforms existing methods on multiple benchmark datasets and achieves significant improvements in indicators such as AUC-ROC, AUC-PR and \({F}_{1}\) score, verifying its effectiveness and robustness in anomaly detection tasks.