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We propose a novel anomaly detection method for echocardiogram videos. The introduced method takes advantage of the periodic nature of the heart cycle to learn three variants of a variational latent trajectory model (TVAE). While the first two variants (TVAE-C and TVAE-R) model strict periodic movements of the heart, the third (TVAE-S) is more general and allows shifts in the spatial representation throughout the video. All models are trained on the healthy samples of a novel in-house dataset of infant echocardiogram videos consisting of multiple chamber views to learn a normative prior of the healthy population. During inference, maximum a posteriori (MAP) based anomaly detection is performed to detect out-of-distribution samples in our dataset. The proposed method reliably identifies severe congenital heart defects, such as Ebstein's Anomaly or Shone-complex. Moreover, it achieves superior performance over MAP-based anomaly detection with standard variational autoencoders when detecting pulmonary hypertension and right ventricular dilation. Finally, we demonstrate that the proposed method enables interpretable explanations of its output through heatmaps highlighting the regions corresponding to anomalous heart structures.