The long-memory temporal dependence of traffic crash fatality for different types of road users

This study investigates the long-memory auto-correlations within daily fatality time series data of the driver, passenger, bicyclist, and pedestrian, and the long-memory cross-correlations between the fatality series of different road users. The analysis is based on the traffic crash fatalities in Florida during the period 1975–2015. A detrended fluctuation analysis (DFA) and a detrended cross-correlation analysis (DCCA) are used for capturing the long-memory auto-correlations and the cross-correlations, respectively. The investigation is conducted through the following steps: (1) identifying the periodicity of the traffic fatalities series via traditional signal processing methods; (2) removing the season effects identified by simple average value analysis and principal component analysis (PCA) from the original time series; (3) based on the original and processed series, exploring the long-memory auto-correlations and cross-correlations in the time series data of different road users. The results of DFA indicate that the auto-correlations of the fluctuations in the daily fatalities are positive for all road users regardless of the seasonal effects. The results of DCCA indicate that the fluctuation in the fatalities for any type of road user is positively associated with that for other road users. The fluctuation in traffic fatalities for any road user is therefore not random-walk but correlated to their fluctuations in the last time unit and that of other road users during the same period. The findings of this study add to the understanding of the long-memory property in traffic fatalities and provide implications for the development of time series models in the traffic safety field.