Urban mobility is on the cusp of transformation with the emergence of shared, connected, and cooperative automated vehicles. Yet, for them to be accepted by customers, trust in their punctuality is vital. Many pilot initiatives operate without a fixed schedule, thus enhancing the importance of reliable arrival time (AT) predictions. This study presents an AT prediction system for autonomous shuttles, utilizing separate models for dwell and running time predictions, validated on real-world data from five cities. Alongside established methods such as XGBoost, we explore the benefits of integrating spatial data using graph neural networks (GNN). To accurately handle the case of a shuttle bypassing a stop, we propose a hierarchical model combining a random forest classifier and a GNN. The results for the final AT prediction are promising, showing low errors even when predicting several stops ahead. Yet, no single model emerges as universally superior, and we provide insights into the characteristics of pilot sites that influence the model selection process. Finally, we identify dwell time prediction as the key determinant in overall AT prediction accuracy when autonomous shuttles are deployed in low-traffic areas or under regulatory speed limits. This research provides insights into the current state of autonomous public transport prediction models and paves the way for more data-informed decision-making as the field advances.