### short-term Goverment Securities Splus

# to read the data

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

# you can make x a regular time series object

x <- rts(x, freq=12)

# plot the data

par(mfrow=c(1,1)) 
ts.plot(x, xlab="Month", ylab="short-term Goverment Securities")

# plot the ACF and PACF

par(mfrow=c(2,2)) 
acf(x)
acf(x, type="partial")

# note the nonstationarity, difference the data

x.diff <- diff(x)

# plot the differenced data

par(mfrow=c(1,1)) 
ts.plot(x.diff, xlab="Month", ylab="differenced short-term Goverment Securities")

# plot the ACF and PACF

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

# ARIMA

# now the ARMA(0,1,1) fit
x.arima <- arima.mle(x, model=list(order=c(0,1,1)), n.cond = 2)
x.arima$model
x.arima$var.coef
x.arima$aic

par(mfrow=c(1,1)) 
arima.diag(x.arima)	

# Forecast 12 time units ahead for ARIMA(0,1,1) model
x.arima.fore <- arima.forecast(x,n=12,model=x.arima$model)
cbind(x.arima.fore$mean,x.arima.fore$std.err)
par(mfrow=c(1,1))
ts.plot(x,x.arima.fore$mean,x.arima.fore$mean+2*x.arima.fore$std.err,
	x.arima.fore$mean-2*x.arima.fore$std.err)