The disclosed embodiments provide a system that performs seasonality-compensated prognostic-surveillance operations for an asset. During operation, the system obtains time-series sensor signals gathered from sensors in the asset during operation of the asset. Next, the system identifies seasonality modes in the time-series sensor signals. The system then determines frequencies and phase angles for the identified seasonality modes. Next, the system uses the determined frequencies and phase angles to filter out the seasonality modes from the time-series sensor signals to produce seasonality-compensated time-series sensor signals. The system then applies an inferential model to the seasonality-compensated time-series sensor signals to detect incipient anomalies that arise during operation of the asset. Finally, when an incipient anomaly is detected, the system generates a notification regarding the anomaly.