In implementations of systems for time-series anomaly detection, a computing device implements an anomaly system to receive, via a network, time-series data describing continuously observed values separated by a period of time. The anomaly system computes updated estimated parameters of a predictive model for the time-series data by performing a rank one update on previously estimated parameters of the predictive model. An uncertainty interval for a future observed value is generated using the predictive model with the updated estimated parameters. The anomaly system determines that an observed value corresponding to the future observed value is outside of the uncertainty interval. An indication is generated that the observed value is an anomaly.