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

•Identify the long-memory property in the crash fatality rate time serie.•Propose an ARFIMA-GARCH model for the long memory property in crash risk analysis.•Reveal factors influencing crash fatality risks and the long-memory property.•The findings benefit the road safety analysis at marco level.