<![CDATA[Background: Forecasting dynamic fuel–equity market correlations is important for financial forecasting because fuel price movements can affect market risk, investor sentiment, and cross-market stability. However, most previous studies focus on direct price or volatility prediction, while the forecasting of rolling correlations between multiple fuel types and global equity indices remains less explored. Objective: This study analyzes and predicts time-varying correlations between global fuel prices and major stock market indices by comparing baseline, PCA-based, standalone deep learning, and hybrid deep learning models. Methods: The proposed framework applies data preprocessing, return transformation, 60-day rolling correlation construction across three fuel variables (petrol, diesel, LPG) and five stock indices (S&P 500, NASDAQ, FTSE 100, Nikkei 225, IHSG/JKSE), normalization, Principal Component Analysis (PCA), sequence generation, and comparative evaluation of 15 forecasting models. Model performance was measured using RMSE, MAE, R-squared (R²), and Directional Accuracy. Results: The PCA Model achieved the lowest RMSE of 0.016909 and the highest R² of 0.967045, while the Persistence Model produced the lowest MAE of 0.002293 and the highest Directional Accuracy of 97.767280%. Hybrid deep learning models showed higher errors and negative R² values, indicating weaker performance on smooth and persistent rolling correlation targets. Conclusion: The findings show that architectural complexity does not necessarily improve forecasting performance when the target series is smooth and persistent. This study contributes empirical evidence and a replicable comparative framework showing that model selection in financial time-series forecasting should consider target characteristics, particularly smoothness and temporal persistence, rather than relying solely on complex deep learning architectures.]]>
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