Asymmetric Peak-Aware Loss for Peak-Critical Time Series Forecasting

Abstract

In many operational time-series forecasting applications, such as crowd demand forecasting, the risk related to under-prediction is substantially higher than that of over-prediction. Accurate prediction of rare demand spikes plays a critical role in downstream tasks. Yet most time-series forecasters are trained with symmetric objectives (e.g., MSE, MAE) and evaluated primarily on aggregate error, which can mask failures in extreme-values and peak-timing predictions. We introduce Asymmetric Peak-Aware Loss (APAL), a simple, model-agnostic objective that (i) penalizes under-predictions more heavily and (ii) increases the training weight of peak regions within each forecast window. We further propose a peak-critical evaluation protocol that complements MAE/MSE with channel-wise tail error (Top-10% and Top-1%) and peak metrics (precision, recall, F1 under timing tolerance, and peak timing error). We evaluate APAL on long-horizon multivariate forecasting across five state-of-the-art backbones, with a focus on pedestrian demand forecasting using (i) a production-ready subset of the City of Melbourne pedestrian hourly count dataset and (ii) a beach visitor count dataset. The generality of the loss function for time-series forecasting is tested on additional benchmarks. Across peak-critical datasets and settings, APAL improves tail accuracy and peak-prediction quality while exposing a controllable trade-off with aggregate error, making it a practical solution when peak-prediction failures are the dominant operational concern.