Financial markets are globally interconnected, and trends in one market frequently influence others
through cross-country spillovers. Forecasting models that overlook these dependencies risk
substantial loss of predictive accuracy. This study proposes a novel hybrid framework that integrates
Wavelet Δ-band decomposition, Light Gradient Boosting Machine (LGBM), and Constricted Particle
Swarm Optimization (CPSO) to forecast Indian stock indices while explicitly modeling cross-country
effects. The target closing price series is decomposed into multi-resolution sub-bands using the
Discrete Wavelet Transform (db4, level 3), and a first-order Δ-transformation is applied to each
reconstructed band to stabilize non-stationarity. Each band is then modeled with CPSO-tuned LGBM
regressors, and predictions are aggregated via inverse DWT. Uniquely, the framework incorporates
U.S. market signals (Dow Jones Industrial Average) alongside 18 domestic technical indicators to
capture global-to-local dependencies across three NSE indices: Nifty-50, Nifty Midcap, and Bank
Nifty. Experimental evaluation on more than ten years of daily data (2013–2025) demonstrates strong
predictive performance, with the Nifty-50 achieving RMSE ≈82.46, MAE ≈57.31, and MAPE
<0.23%. SHAP-based interpretability analysis attributes approximately 47.68% of feature importance
to cross-country indicators, confirming significant global influence. A comprehensive ablation study
validates the incremental contribution of each component, and Diebold–Mariano tests establish
statistically significant improvements over baseline ML, deep learning, and econometric benchmarks,
highlighting both methodological novelty and practical value for investors and policymakers.