Anomaly detection is an essential component for ensuring the safety and reliability of critical systems. Currently, most machine learning-based anomaly detection approaches rely purely on correlations among sensor signals, rather than causal relations, making them susceptible to spurious associations. This limitation can lead to poor generalization and unreliable anomaly detection in practical scenarios. To address this, we propose an anomaly detection approach which leverages score-based causal discovery, NTS-DAGMA. This causal discovery method advances over prior work by combining the network architecture from NTS-NOTEARS with the acyclicity constraint from DAGMA. Like other prediction-based anomaly detection methods, it can predict future states; however, it does this by learning and utilizing causal relations in the time series data. Through comprehensive experiments, we demonstrate that: (i) on causal discovery tasks NTS-NOTEARS and NTS-DAGMA achieve similar performances; (ii) on anomaly detection tasks NTS-NOTEARS and NTS-DAGMA also perform similar to each other, and have comparable performance to state-of-the-art ML approaches; and (iii) most importantly, our results show that NTS-DAGMA provides causally meaningful models: detects anomalies which propagate through child nodes in agreement with the inferred causal graph. Incorporating causal structure into the model enables improved interpretability and aligns anomaly detection with the physical dynamics of the system.