# Example 1.12 in notes; oil price data, log-transformed
data(oil.price)
n=length(oil.price)
n.ahead=24
xo=data.frame(t=1:n,t2=(1:n)^2)
f=arima(log(oil.price),order=c(0,1,1),xreg=xo)
xf=data.frame(t=(n+1):(n+n.ahead),t2=((n+1):(n+n.ahead))^2)
plot(f,n.ahead=n.ahead,newxreg=xf,
 ylab='Oil Price',xlab='Year',n1=c(2000,1),transform=exp)

# thermal data from midterm, quadratic trend
y=ts(read.table("http://people.stat.sc.edu/hansont/stat520/thermal.txt"),start=1)
n=length(y)
n.ahead=20
xo=data.frame(t=1:n,t2=(1:n)^2)
f=arima(y,order=c(0,1,1),xreg=xo)
f
xf=data.frame(t=(n+1):(n+n.ahead),t2=((n+1):(n+n.ahead))^2)
plot(f,n.ahead=n.ahead,newxreg=xf,
 ylab='temp',xlab='day',n1=100)

# thermal data, linear trend
xo=data.frame(t=1:n)
f=arima(y,order=c(0,1,1),xreg=xo)
f
xf=data.frame(t=(n+1):(n+n.ahead))
plot(f,n.ahead=n.ahead,newxreg=xf,
 ylab='temp',xlab='day',n1=100)

# thermal data, no trend
f=arima(y,order=c(0,1,1))
f
plot(f,n.ahead=n.ahead,
 ylab='temp',xlab='day',n1=100)