Climate change, the scarcity of fossil fuels, advances in clean energy, and volatility of crude oil prices have led to the recognition of clean energy as a viable alternative to dirty energy. This paper investigates the multifractal scaling behavior and efficiency of green finance markets, as well as traditional markets such as gold, crude oil, and natural gas between 1 January 2018, and 9 March 2023. To test the serial dependency (autocorrelation) and the efficient market hypothesis, in its weak form, we employed the Lo and Mackinlay test and the DFA method. The empirical findings showed that returns data series exhibit signs of (in)efficiency. Additionally, there is a negative autocorrelation among the crude oil market, the Clean Energy Fuels Index, the Global Clean Energy Index, the gold market, and the natural gas market. Arbitration strategies can be used to obtain abnormal returns, but caution should be exercised as prices may increase above their actual market value and reduce the profitability of trading. This work contributes to the body of knowledge on sustainable finance by teaching investors how to use predictive strategies on the future values of their investments.