# Seatbelts

Documentation

## 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.

### Usage

UKDriverDeaths
Seatbelts


### Format

Seatbelts is a multiple time series, with columns

DriversKilled

car drivers killed.

drivers

same as UKDriverDeaths.

front

front-seat passengers killed or seriously injured.

rear

rear-seat passengers killed or seriously injured.

kms

distance driven.

PetrolPrice

petrol price.

VanKilled

number of van (‘light goods vehicle’) drivers.

law

0/1: was the law in effect that month?

### Source

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. http://www.ssfpack.com/dkbook/

### References

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.

### Examples

require(stats); require(graphics)
## 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)

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