Road Casualties in Great Britain 1969–84
UKDriverDeaths is a time series giving the monthly totals
of car drivers in
Great Britain killed or seriously injured Jan 1969 to Dec 1984.
Compulsory wearing of seat belts was introduced on 31 Jan 1983.
Seatbelts is more information on the same problem.
Seatbelts is a multiple time series, with columns
car drivers killed.
front-seat passengers killed or seriously injured.
rear-seat passengers killed or seriously injured.
number of van (‘light goods vehicle’)
0/1: was the law in effect that month?
Harvey, A.C. (1989)
Forecasting, Structural Time Series Models and the Kalman Filter.
Cambridge University Press, pp. 519–523.
Durbin, J. and Koopman, S. J. (2001) Time Series Analysis by
State Space Methods. Oxford University Press.
Harvey, A. C. and Durbin, J. (1986) The effects of seat belt
legislation on British road casualties: A case study in structural
time series modelling. Journal of the Royal Statistical Society
series B, 149, 187–227.
## work with pre-seatbelt period to identify a model, use logs
work <- window(log10(UKDriverDeaths), end = 1982+11/12)
par(mfrow = c(3, 1))
plot(work); acf(work); pacf(work)
par(mfrow = c(1, 1))
(fit <- arima(work, c(1, 0, 0), seasonal = list(order = c(1, 0, 0))))
z <- predict(fit, n.ahead = 24)
ts.plot(log10(UKDriverDeaths), z$pred, z$pred+2*z$se, z$pred-2*z$se,
lty = c(1, 3, 2, 2), col = c("black", "red", "blue", "blue"))
## now see the effect of the explanatory variables
X <- Seatbelts[, c("kms", "PetrolPrice", "law")]
X[, 1] <- log10(X[, 1]) - 4
arima(log10(Seatbelts[, "drivers"]), c(1, 0, 0),
seasonal = list(order = c(1, 0, 0)), xreg = X)