UK road accidents. Long run trends and persistence using fractional integration

• Trends and persistence of road accidents in the UK are examined in this work. • Fractional integration is the methodology used • Traditional models often fail to capture long-term effects. • By applying fractional integration, this study investigates the persistence of traffic accidents over time. • Findings provide insights into the effectiveness of past interventions for reducing accidents and improving road safety. This study analyses long-term trends and persistence in road traffic accidents in the United Kingdom using fractional integration models. Although numerous interventions have been implemented to reduce accident rates, persistent effects and temporal dynamics have received little attention, especially in accidents involving pedestrians, cyclists and drivers. Traditional approaches, based on integer differentiation, do not adequately capture these prolonged dependencies, limiting understanding of the underlying processes. Fractional integration allows for the modelling of non-stationary series with mean reversion, offering a more accurate representation of the temporal structure and persistence in the data. The results show high persistence in cyclist and pedestrian deaths, indicating that temporary interventions are insufficient to achieve sustainable reductions in accident rates. These conclusions have direct implications for public policy formulation: permanent strategies are required that include investments in safe infrastructure (segregated lanes, improved pedestrian crossings), continuous enforcement of speed limits and regulations, and monitoring systems differentiated by user type. Overall, the study provides empirical evidence on the need for structural and sustained approaches to reduce accidents.