This paper deals with the analysis of trends in road accidents on highways in Brazil. We use time series techniques based on fractional integration that allow us to determine if exogenous shocks in the data have transitory or permanent effects depending on the order of integration of the series. Our results indicate that a low degree of long memory was detected in the series with shocks having thus transitory effects over time. We further find that the number of accidents have been reducing over time, though in the presence of negative shocks, the recovery is not going to be immediate due to the long memory nature of the data. Despite the absence of relevant investment relating to infrastructure expansion, it is worth mentioning the consolidation of a nationwide tolled road system in Brazil involving concessions to private administrators, alongside more severe traffic laws that can impose limitations on driving licences.