### Airline passenger data R

library(ts)

# read the data

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

# you can make x a regular time series object

x <- ts(x, start=c(1949,1), freq=12)

# plot the data

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

# log

x.log <- log(x)

# plot the data

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

# difference

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

# plot the data

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

# ACF and PACF

win.graph()
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

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

# ACF and PACF

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

# Fit model

x.log.sarima <- arima0(x.log, order=c(0,1,1), seasonal = list(order=c(0,1,1), period=12))
x.log.sarima

win.graph()
par(mfrow=c(3,1))
ts.plot(x.log.sarima$resid)
acf(x.log.sarima$resid,48)
acf(x.log.sarima$resid,48,type="partial")