The disclosed embodiments provide a system that detects anomalous events in a virtual machine. During operation, the system obtains time-series garbage-collection (GC) data collected during execution of a virtual machine in a computer system. Next, the system generates one or more seasonal features from the time-series GC data. The system then uses a sequential-analysis technique to analyze the time-series GC data and the one or more seasonal features for an anomaly in the GC activity of the virtual machine. Finally, the system stores an indication of a potential out-of-memory (OOM) event for the virtual machine based at least in part on identifying the anomaly in the GC activity of the virtual machine.