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The global energy transition has created unprecedented linkages between precious metals markets and renewable energy sectors. This study examines the relationship between gold prices, silver prices, and global solar energy capacity over 2005-2024 using ARIMA and Vector Error Correction Model (VECM) methodologies. The analysis reveals statistically significant short-term relationships where silver prices (p < 0.01) and solar capacity (p = 0.014) influence gold price movements. The VECM identifies cointegrating relationships among variables, with solar capacity showing high explanatory power (R² = 0.97). However, the limited sample size (n=20) and potential specification issues require cautious interpretation. These findings contribute to understanding commodity-energy market integration during structural transformation periods, with implications for portfolio management and energy transition finance. The results suggest that precious metals markets have incorporated renewable energy information as fundamental pricing factors, though the economic significance and stability of these relationships warrant further investigation with larger datasets.