Capturing long-memory properties in road fatality rate series by an autoregressive fractionally integrated moving average model with generalized autoregressive conditional heteroscedasticity: A case study of Florida, the United States, 1975–2018

Introduction: Time series models play an important role in monitoring and understanding the serial dynamics of road crash exposures, risks, outcomes, and safety performance indicators. The time-series methods applied in previous studies on crash time series analysis assume that the serial dependency decays rapidly or even exponentially. However, this assumption is violated in most cases because of the existence of long-memory properties in the crash time series data. Ignoring the long-memory dependency could result in biased understanding of the dynamics of road traffic crashes. Method: To fill this research gap, this study proposes an autoregressive fractionally integrated moving average model with generalized autoregressive conditional heteroscedasticity (ARFIMA-GARCH) to capture and accommodate the long-memory decencies in the road fatality rate time series. To further investigate how the factors influencing the fatality risks play a role in the long-memory dependence, the effects of exogenous variables are examined in this study. The analysis is conducted based on the road crash fatality data in Florida, USA over 44 years. Results’ Conclusions: The case analysis confirmed the existence of long-memory property in the crash fatality time series data by both the joint tests of Augmented Dickey-Fuller and the Phillips–Perron, and the integer order of differencing (≤0.5) in the proposed models. The model results reveal that gasoline price and alcohol consumption per capita is positively associated with road fatality risks, whereas unemployment rate and rural/urban road mileage are negatively related to the road fatality risks. Practical Applications: The significant influential factors are also found to account for the long-memory serial correlations between road traffic fatalities to some extent.