### short-term Goverment Securities R

library(ts)

# to read the data

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

# you can make x a regular time series object

x <- ts(x, freq=12)

# plot the data

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

# plot the ACF and PACF

win.graph()
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

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

# plot the ACF and PACF

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

# ARIMA

# now the ARMA(0,1,1) fit

x.arima <- arima0(x, order=c(0,1,1))
summary(x.arima)

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

# Forecast 12 time units ahead for ARIMA(0,1,1) model

x.arima.fore <- predict(x.arima,n.ahead=12)
cbind(x.arima.fore$pred,x.arima.fore$se)
win.graph()
par(mfrow=c(1,1))
ts.plot(x,x.arima.fore$pred,x.arima.fore$pred+2*x.arima.fore$se,
	x.arima.fore$pred-2*x.arima.fore$se)