A strategy is described for identifying anomalies in time-series data. The strategy involves dividing the time-series data into a plurality of collected data segments and then using a modeling technique to fit local models to the collected data segments, Large deviations of the time-series data from the local models are indicative of anomalies In one approach, the modeling technique can use an absolute value (L1) measure of error value for all of the collected data segments. In another approach, the modeling technique can use the L1 measure for only those portions of the time-series data that are projected to be anomalous. The modeling technique can use a squared-term (L2) measure of error value for normal portions of the time-series data. In another approach, the modeling technique can use an iterative expectation-maximization strategy in applying the L1 and L2 measures.