Robust Time Series Forecasting via Bounded Kernel Loss

Time series forecasting models predominantly rely on Mean Squared Error (MSE) optimization, which fundamentally assumes independent, identically distributed Gaussian residuals. However, in real-world scenarios, the complex interplay between inherent data noise (aleatoric uncertainty) and model capacity limits (epistemic uncertainty) frequently yields asymmetric, heavy-tailed error distributions. Under MSE's unbounded quadratic penalty, these unlearnable extreme residuals disproportionately dominate the gradient updates, forcing the model to overfit noise and severely degrade generalization. To resolve this fundamental misalignment, we propose a robust optimization framework centered on Bounded Kernel Loss (BKLoss). Rather than penalizing all errors uniformly, BKLoss evaluates prediction quality through localized Gaussian-kernel similarity. This mechanism naturally caps the gradient contribution of extreme outliers, allowing the model to dynamically assign lower weights to unlearnable deviations and focus its capacity on generalizable patterns. We further develop a Top-$\beta$ Mean Adaptive Strategy that dynamically calibrates the batch-wise kernel bandwidth based on the residual statistics. Supported by theoretical analysis of the loss formulation and gradient boundedness, extensive experiments across multiple benchmark datasets demonstrate that our method consistently outperforms strong baselines, achieving highly stable forecasting performance in highly uncertain environments. The code is provided in the supplementary material.