<p>Anomaly detection for multivariate time series is crucial in real-world applications, including industrial equipment monitoring and predictive maintenance, financial risk management, smart city and traffic management, as well as environmental monitoring. However, the multivariate time series data exhibit high dimensionality, complex spatiotemporal dependencies, and nonlinear interactions between variables, making anomaly detection in such data a significant challenge. Most existing methods struggle to effectively capture these complex nonlinear relationships or explicitly model the spatiotemporal dependencies in multivariate time series. To address these limitations, we propose a novel approach for multivariate time series anomaly detection, called long short-term memory, temporal convolution and graph convolution (LTG), which is based on spatial-temporal graph learning. LTG uses Correlation Learning (CL) layer to acquire pairwise correlations, generating a graph adjacency matrix. This matrix is then fed into a Spatiotemporal Graph Neural Network (STGNN), composed of a Long Short-Term Memory (LSTM) Network, a Temporal Convolution Network (TCN), and a Graph Convolution Network (GCN), to capture the rich temporal and spatial dependencies in multivariate time series and accurately model these relationships. Finally, a PCA-based anomaly scorer is employed to output anomaly scores. Experimental results show that on the WADI and SMD datasets, LTG outperforms the state-of-the-art multivariate anomaly detection framework correlation-aware spatial-temporal graph learning (CST-GL) in both overall detection and early detection performance. Notably, on the WADI dataset, LTG’s average early detection performance across 6 different delay-constrained time points exceeds CST-GL by 10.64 percentage points.</p>