This study applies intermarket analysis to forecast the New Zealand NZX 50 stock returns using a hybrid framework that combines econometric models with machine learning (ML) algorithms. Daily return data from 3 January 2001 to 31 December 2024 are employed to examine the interconnectedness between the New Zealand equity market and major global financial markets. This study follows a three-stage methodology: ML-based feature selection using LASSO, ridge, and elastic net regressions; econometric validation through a Global Vector Autoregressive (GVAR) model; and forecasting implementation using Support Vector Regression (SVR), Random Forest (RF), Long Short-Term Memory, and Artificial Neural Networks. Feature selection consistently identifies the Australian ASX 200, Japanese Nikkei 225, U.S. S&P 500, and U.S. 10-year Treasury yield as the most influential predictors, with Australia exerting the strongest impact. GVAR results reveal significant short-term spillover effects, but no long-term co-integrating relationships, indicating independent market trends. The U.S. market emerges as the dominant transmitter of shocks, while New Zealand acts as a net receiver. Forecasting results show RF and SVR outperform alternative models, with optimal performance achieved using a fifth-lag structure. The findings support short-term, spillover-based investment strategies and contribute to a transparent, replicable framework for forecasting equity markets in small open economies.