# Example for model identification and forecasting #
# Generate some training data from ARIMA(2,1,2)
set.seed(1)
series2 <- arima.sim(model=list(order=c(2,1,2), ar=c(.4, .2), ma=c(.3,.1)), , n=100)
series1 <- ts(series2[1:90])

# Graph the data.
par(mfrow=c(3,2))
plot(series1)
title("ARIMA(2,1,2)")
plot(diff(series1))
title("Differenced")
acf(series1)
acf(diff(series1))
acf(series1, type="partial")
acf(diff(series1), type="partial")

# fit ARIMA model to first 90 observations
fit <- arima(series1, order=c(2,1,2))

# and compute forecasts for last 10.
pred <- predict(fit, n.ahead=10)

# graph them.
par(mfrow=c(1,1))
plot(c(series1,pred$pred), ylim=c(-3,50), type="n")
lines(1:90,series1, lty=1)
points(91:100, pred$pred, pch=3) #These are the forecasts
lines(91:100, pred$pred + 2*pred$se, lty=2) #These are the forecast intervals
lines(91:100, pred$pred - 2*pred$se, lty=2)
points(91:100, series2[91:100], pch=1) #This is the data that was "held out"
title("95% Forecast intervals")