In this paper, focus is on finding a suitable model for the annual Zimbabwe Traffic Accident statistics from 1997 to 2013 and to forecast the number of annual traffic accidents likely to occur in future. The Box-Jenkins model building strategy is used. The Augmented Dickey Fuller test showed that the accident data was non-stationary. After first order differencing, the data became stationary. Three ARIMA models were suggested based on the ACF and PACF plots of the differenced series, these were ARIMA(0,1,0), ARIMA(1,1,0) and ARIMA(1,1,1). The model with the smallest corrected Akaike Information Criteria (AICc) and Bayesian Information Criteria (BIC) was chosen as the best model. The Ljung-Box statistics among others were used in assessing the quality of the model. ARIMA (0,1,0) was the best model for the Zimbabwe annual Traffic Accident data. Forecasting retained the value at the forecast origin. The implications of these findings are that based on the annual road traffic accident data for the period under consideration, it is difficult to make reasonable forecasts of the number of road traffic accidents for the years ahead of 2013. This is due to the fact that the values at different times of a white noise process are statistically independent.
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