Forecasting Transformed Series

Procedure

Forecasting involves special considerations when dealing with transformed series:

• Differencing: Forecasting nonstationary series or forecasting stationary differenced series and then “undoing” the difference yields the same forecasts.
• Log Transformations: For $Z_t=\ln (Y_t)$:
  • The naive forecast $\exp ({\hat{Z}}_t(l))$ minimizes the mean absolute error (this is optimal for the lognormal median).
  • The minimum mean square error forecast is: $\exp \left\{{\hat{Z}}_t(l)+\frac{1}{2}Var[e_t(l)]\right\}$