New company registrations (per 100,000 popn) in New Zealand

Use this diagram to illustrate use of the AR(1) model for time series with trend.

Initially the series is not detrended before use of the model. The three buttons change the line that is used to forecast each value from the previous value. (Least squares is best.) The blue lines on the time series plot show the forecasts.

(You could mention that the least squares forecasting line has slope greater than one, so when it is used to forecast beyond the end of the series, the forecasts increase exponentially. If the slope had been less than one, the forecasts would have exponentially decreased towards the sample mean.)

Use the pop-up menu to remove a quadratic trend before using the AR(1) model. In other words, the AR(1) model is applied to the residuals. Click the Least squares button to give the best forecasts. Since the intercept is relatively small, the forecast for each detrended value is approx 70% of the previous detrended value.

The data set shows the rate of new company registrations in New Zealand (per 100,000 population) between 1960 and 1998.