# Example for model identification and forecasting #
# Generate some training data from AR(1) or ARIMA(1,0,0)
set.seed(1)
series1a <- arima.sim(model=list(order=c(1,0,0), ar=0.8), n=100)
series1 <- ts(series1a[1:90])

# Graph the data.
par(mfrow=c(3,1))
plot(series1a)
title("AR(1))")
acf(series1)
acf(series1, type="partial")

# fit ARIMA model to first 90 observations
fit <- arima(series1, order=c(1,0,0))

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


# graph them.
par(mfrow=c(1,1))
plot(c(series1,pred$pred), ylim=c(-4,4), type="n")
lines(1:90,series1, lty=1)
points(series1, pch=1)
points(pred$pred, pch=3)
lines(91:100, pred$pred + 2*pred$se, lty=2)
lines(91:100, pred$pred - 2*pred$se, lty=2)
points(91:100, series1a[91:100], pch=1)
title("95% Forecast intervals")
legend("topleft", c("data", "forecasts"), pch=c(1,3))