Forecasting when there is trend

The method described in the previous page works well if there is no trend in the time series. If there is trend, we should remove it before using an AR(1) model. The steps for forecasting a future value are therefore...

  1. Estimate the trend in the series.
  2. Fit an AR(1) model to the detrended values (residuals).
  3. Forecast future detrended values by applying the AR(1) model to the most recent detrended value.
  4. Forecast the trend (using the model fitted in step 1) and add the detrended forecast from step 3.

(There are more efficient ways to do steps 1 and 2 together, but these are beyond the scope of an introductory course.)