The paper reports analyses of road accident data in Britain in which time series of monthly accident data for the period 1970-1978 have been related to a number of explanatory variables. Two sets of results are presented. Two-vehicle accidents were modelled by regression; because the time trends in this data appeared to be reasonably consistent, the resulting model was regarded as adequate. In the case of single-vehicle accidents, trends were not consistent over the period, and it was considered that the Box-Jenkins time series method might be more appropriate than simple regression. The principles involved in fitting Box-Jenkins models to this data are explained and the results compared with the regression method. The tentative conclusion drawn from this comparison is that because accident series are generally very "noisy" and autocorrelation among the residuals from standard regressions not very strong, Box-Jenkins models are unlikely to represent the series appreciably better than regression based on the assumption of uncorrelated residuals. Predictions of the alternative models for the years 1979-1981 are presented and discussed.