New Loss Function Improves Peak Prediction in Time Series

This research addresses a critical limitation in many operational time-series forecasting applications: the accurate prediction of rare demand spikes, where under-prediction carries substantially higher risk than over-prediction. Traditional time-series forecasters often rely on symmetric objectives like Mean Squared Error (MSE) or Mean Absolute Error (MAE), which tend to mask failures in predicting extreme values and peak timing. The authors introduce Asymmetric Peak-Aware Loss (APAL), a simple yet powerful model-agnostic objective function. APAL operates on two core principles: first, it applies a heavier penalty to under-predictions, reflecting the higher cost associated with missing a demand surge. Second, it strategically increases the training weight of peak regions within each forecast window, ensuring the model pays closer attention to these critical events. Alongside APAL, the paper proposes a new peak-critical evaluation protocol that complements standard MAE/MSE metrics. This protocol includes channel-wise tail error (Top-10% and Top-1%) and specific peak metrics such as precision, recall, F1 score under timing tolerance, and peak timing error. Evaluations across five state-of-the-art backbones, particularly on pedestrian demand forecasting datasets (City of Melbourne and a beach visitor count), demonstrate APAL's effectiveness. It consistently improves tail accuracy and peak-prediction quality, offering a controllable trade-off with aggregate error, making it an ideal solution for scenarios where peak-prediction failures are a dominant operational concern.