### Airline passenger data Splus

# read the data

x <- scan("E:\\Stat207\\Midterm\\Airpass.dat")

# you can make x a regular time series object

x <- rts(x, start=c(1949,1), freq=12, units="years")

# plot the data

par(mfrow=c(1,1)) 
ts.plot(x, xlab="Year", ylab="Airline Passengers")

# log

x.log <- log(x)

# plot the data

par(mfrow=c(1,1)) 
ts.plot(x.log, xlab="Year", ylab="log Airline Passengers")

# differecne

x.log.diff <- diff(x.log)

# plot the data

par(mfrow=c(1,1)) 
ts.plot(x.log.diff, xlab="Year", ylab="differenced log Airline Passengers")

# ACF and PACF

par(mfrow=c(2,2))
acf(x.log.diff,48)
acf(x.log.diff,48,type="partial")

# seasonal difference

x.log.diff.diff12 <- diff(x.log.diff,12)

# plot the data

par(mfrow=c(1,1)) 
ts.plot(x.log.diff.diff12, xlab="Year", ylab="seasonal differenced log Airline Passengers")

# ACF and PACF

par(mfrow=c(2,2))
acf(x.log.diff.diff12,48)
acf(x.log.diff.diff12,48,type="partial")

# 

x.log.model <- list(list(order=c(0,1,1)), list(order=c(0,1,1), period=12))
x.log.sarima <- arima.mle(x.log, model=x.log.model)
x.log.sarima
x.log.sarima$model
par(mfrow=c(1,1))
arima.diag(x.log.sarima,lag=48)