#identify the model for the natural process over the pre-intervention period
plot(window(log(airmiles),end=c(2001,8)))
plot(window(diff(log(airmiles),1),end=c(2001,8)))
acf(window(diff(log(airmiles),1),end=c(2001,8)),lag.max=48)
acf(window(diff(diff(log(airmiles),1),lag=12),end=c(2001,8)),lag.max=48)
pacf(window(diff(diff(log(airmiles),1),lag=12),end=c(2001,8)),lag.max=48)
eacf(window(diff(diff(log(airmiles),1),lag=12),end=c(2001,8)))


arima1=arimax(log(airmiles),order=c(0,1,1),seasonal=list(order=c(0,1,0)))
arima1
tsdiag(arima1)
arima2=arimax(log(airmiles),order=c(0,1,1),seasonal=list(order=c(0,1,1)))
arima2
tsdiag(arima2)

arima3=arimax(log(airmiles),order=c(0,1,1),seasonal=list(order=c(0,1,1)),
xtransf=data.frame(I911=1*(seq(airmiles)==69),
I911=1*(seq(airmiles)==69)),
transfer=list(c(0,0),c(1,0)))
arima3

# half-life
-log(2)/log(.89)
tsdiag(arima3)