This study examines the relationship between crude oil, a proxy for brown energy, and several renewable energy stock sector indices (e.g., solar energy, wind energy, bioenergy, and geothermal energy) over various investment horizons. Using daily data from October 15, 2010, to February 23, 2022, we apply a combination of methods involving co-integration, wavelet coherency, and wavelet-based Granger causality. The results show that the relationship between crude oil and renewable energy indices is non-linear and somewhat multifaceted. Firstly, there are sectorial differences in the intensity of the relationships. Notably, the relationship intensity between the wind and crude oil is lower than that involving geothermal energy or bioenergy. Secondly, the relationship evolves with time. For example, the COVID-19 outbreak seems to have increased the relationship between crude oil and renewable energy markets, notably for solar, bioenergy, and geothermal. Thirdly, the relationship varies across scales. When controlling for the VIX (volatility index), a proxy of the sentiment of market participants, and EPU (economic policy uncertainty index), the relationship seems strong in the long term but weak in the short term. This result is confirmed using a Granger causality test on the wavelet-decomposed series. These findings have important implications for long-term investors, short-term speculators, and policymakers regarding the co-movement between brown and renewable energy markets.