Unified Loss-Level Regularization for Spike-Aware and Anti-Lag Time Series Forecasting

Time-series forecasting in safety and regulation-critical domains is frequently degraded by two systematic deficiencies of neural sequence models: persistence-induced temporal lag and reduced sensitivity to rare yet high-impact spikes. This work addresses both limitations at the loss-function level. We introduce a unified, architecture-agnostic training framework that augments standard regression losses with spike-aware and anti-lag objectives applied to residual predictors instantiated on LSTM, GRU, and TCN backbones. Spike sensitivity is promoted through volatility-weighted regression, an auxiliary spike-classification head, and the use of volatility-sensitive evaluation metrics that emphasize highly dynamic regimes. Anti-lag behavior is encouraged via derivative matching, a zero-lag preference term, and multi-lag decorrelation, jointly aligning predictions with both the magnitude and timing of rapid transitions while mitigating persistence bias. Across three real-world case studies—CO \(_2\) in aquaculture systems, Brisbane River water quality, and indoor temperature control—the proposed objective consistently reduces lag and improves RMSE-family metrics and spike F1 relative to strong baselines, without requiring architectural modifications or incurring additional inference-time cost. Consequently, the proposed loss-level regularization transforms generic sequence models into volatility-aware, real-time forecasters that remain robust in smooth regimes and are better suited to environmental and industrial monitoring applications.