The complex trajectories of higher education students are deviations from the regular path due to delays in completing a degree, dropping out, taking breaks, or changing programmes. In this study, we investigated degree changing as a cause of complex student trajectories. We characterised cohorts of students who graduated with a complex trajectory and identified the characteristics that influenced the time to graduation. To support this predictive task, we employed machine learning techniques such as neural networks, support vector machines, and random forests. In addition, we used interpretable techniques such as decision trees to derive managerial insights that could prove useful to decision-makers. We validated the proposed methodology taking the University of Porto (Portugal) as case study. The results show that the time to degree (TTD) of students with and without complex trajectories was different. Moreover, the proposed models effectively predicted TTD, outperforming two benchmark models. The random forest model proved to be the best predictor. Finally, this study shows that the factors that best predict TTD are the median TTD and the admission regime of the programme of destination of transfer students, followed by the admission average of the previous programme. By identifying students who take longer to complete their studies, targeted interventions such as counselling and tutoring can be promoted, potentially improving completion rates and educational outcomes without having to use as many resources.