<p>Multivariate time series anomaly detection is essential in industrial systems for early fault diagnosis and predictive maintenance. Recent advances in deep learning have significantly improved the modeling of Spatio-Temporal dependencies, thereby enhancing anomaly detection performance. However, existing approaches still face critical challenges: inadequate modeling of deep sensor-level dependencies and the adverse effects of nonstationarity in time series, which hinder prediction accuracy and model generalization. To address these issues, we propose a novel framework for multivariate time series anomaly detection based on a Stationary Spatio-Temporal Constrained Graph Model (SSTCG). This framework integrates both spatial and temporal modeling innovations. For spatial dependency modeling, we introduce the Constraint-Driven Dynamic and Static Graph Networks (CDDS), which jointly learn a pair of graph structures. The static graph captures global shared spatial dependencies across all sequences, while the dynamic graph models sample-specific relationships. By maximizing the discrepancy between these two graphs under mutual constraints, the dynamic graph retains unique structural characteristics, and the static graph encodes invariant dependencies, allowing for a more precise and discriminative spatial representation. For temporal modeling, we design a Stationary Hierarchical Unet model (SHU). This model addresses non-stationarity by normalizing and slicing the input time series into patches, which are then embedded with positional encoding. A hierarchical U-Net architecture extracts multiscale temporal features using MLP blocks at each layer to capture channel-wise interactions. To explicitly restore the original statistical characteristics of the time series, we propose a stationarity correction mechanism that adjusts the predicted output values to minimize the difference in autocorrelation matrices between the input and output. This not only mitigates non-stationarity but also preserves the temporal dependencies within the sequence. Finally, the anomaly score is calculated according to the deviations among the predicted and observed values, and anomalies are detected using a threshold-based decision function. Widespread experiments on a large number of real-world datasets have shown that the SSTCG framework is effective in capturing fine-grained spatio-temporal patterns and enhancing anomaly detection accuracy.</p>