This paper examines the efficiency, in its weak form, of the clean energy stock indices, Clean Coal Technologies, Clean Energy Fuels, and Wilderhill, as well as the cryptocurrencies classified as "dirty", due to their excessive energy consumption, such as Bitcoin (BTC), Ethereum (ETH), Ethereum Classic (ETH Classic), and Litecoin (LTC), from January 2020 to May 30, 2023. In order to meet the research objectives, the aim is to answer the following research question, namely whether: i) the events of 2020 and 2022 accentuated the persistence in the clean energy and dirty energy indices? The results show that clean energy indices such as digital currencies classified as "dirty" show autocorrelation in their returns; the prices are not independent and identically distributed (i.i.d). In conclusion, arbitrage strategies can be used to obtain abnormal returns, but caution is needed as prices can rise above their real market value and reduce trading profitability. This study contributes to the knowledge base on sustainable finance by teaching investors how to use forecasting strategies on the future values of their investments.