The objectives achieved in the Paris Agreement to reduce greenhouse gas emissions and reduce dependence on fossil fuels have caused, in recent years, a growing importance on sustainability in companies in order to reduce Environmental, social and economic impacts. This study is focused on understanding how the variation in West Texas Intermediate crude oil prices affects the Dow Jones Sustainability Index, and therefore the companies included in it, and vice versa. The research aims to examine the statistical properties of both indices, using fractional integration methods, the fractional cointegration vector autoregressive (FCVAR) approach and the continuous wavelet transform (CWT) technique. The results warn of a change in trend, with the application of extraordinary measures being necessary to return to the original trend, while the analysis of cointegration and wavelet analysis measures reflect that an increase in those adopted based on sustainability by the different companies that make up the index imply a drop in the price of crude oil.

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