This paper deals with the analysis of the evolution of international trade after COVID-19, examining commodity prices, the shipping industry, and the influence of the cost of bunker fuel. To this end, we use techniques based on fractional integration, fractional cointegration VAR (FCVAR) and wavelet analysis. Monthly data relating to heavy fuel oil prices and the shipping market from October 2011 to September 2021 are used. Using fractional integration in the post-break period, a lack of mean reversion is observed in all cases, which means that, for the commodity prices and shipping market indices, a change in trend will be permanent after COVID-19 unless strong measures are carried out by the authorities. Using wavelet analysis, we conclude that the demand shock represented in the indices mentioned above has led the price of fuel oil since the beginning of the pandemic, and bunker fuel is not relevant in determining the cost of maritime transport.