Traffic accidents involve great costs both at an economic and a human level. This demands that governments implement strategies to reduce their number and impact. The knowledge of the nature of the phenomenon through the study of time series of accidents enables the design of suitable policies for the desired objectives to be achieved. Thus, this paper deals with the analysis of the statistical properties of the number of road accidents on Spanish roads by using time series techniques based on the concept of fractional integration. The results indicate that the series examined display very low degrees of persistence, with the orders of integration being around 0 and thus showing a short memory pattern. This implies that shocks will be transitory, disappearing fast, and requiring strong policy measures in the case of positive shocks that reduce the number of deaths if we want to maintain that effect in the long run.