Forecasting performance measures for traffic safety using deterministic and stochastic models

Traffic-safety performance measures required by the Moving Ahead Progress in 21st Century (MAP-21) act were forecasted in this study to facilitate the reduction of fatalities and serious injuries. Given the lack of exposure data (e.g., traffic counts), time series were used to conduct the forecast. Deterministic and stochastic models were applied using four independent and univariate time series from the crash data collected by the Nevada Department of Transportation. The best model specification was obtained using root mean square error and mean absolute percent prediction error as goodness of fit. Among several deterministic models evaluated in this study, the Winter-additive model for seasonal data and the Damped-trend model for non-seasonal data provided adequate forecasts. In the case of stochastic models, for non-seasonal data, an Autoregressive Integrated Moving Average (ARIMA) model provided acceptable results. However, the absence of adequate data likely precludes an appropriate estimation using the ARIMA model. For seasonal data, a Seasonal Autoregressive Integrated Moving Average (SARIMA) model provided the best forecast measures. The stochastic SARIMA(0,0,5)(0,1,1)12 model, an improved model, had a preferred fit for predicting the number of fatalities and serious injuries in Nevada over a five-year horizon. The SARIMA model could be an appropriate statistical model to predict fatalities and serious injuries as required by MAP-21.