Econometric-prior-guided multi-head attention with application for interpretable multi-horizon financial forecasting

Reliable financial forecasting requires both predictive accuracy and transparent model behavior. This study presents Economic-Loss Guided Multi-Head Self-Attention (ELG-MHSA), a transformer framework that regularizes three attention heads toward distinct econometric and statistical priors: GARCH-based conditional variance, a trailing moving-average target for mean reversion, and a one-sided trend estimate. The priors are constructed separately within each causal input window and are normalized over eligible historical positions only, preventing future information from entering training or evaluation. The proposed losses are optimized jointly with the forecasting objective without changing the transformer encoder structure. Experiments on VIX Futures, FRED-MD, and Binance BTC-USD compare ELG-MHSA with GARCH(1,1), EGARCH, a standard multi-head transformer, and the Temporal Fusion Transformer. The reported results are interpreted as descriptive performance differences unless accompanied by formal uncertainty estimates. The framework is intended to improve the economic interpretability of attention while retaining multi-horizon predictive capacity.