The Root Mean Square Error (RMSE) during the validation period is 1.00, while the  Mean Absolute Scaled Error (MASE) is 0.95, this means that when comparing with the naive forecast (\(Y(t+1)=Y(t)\))  the predicted values  using the transfer function model provide an improvement over the naive forecast. Considering that the training period in this case (1900-1953) is much shorter in comparison with the training period used for the ES method (1800-1953), the transfer function model provides a competitive approach as a forecasting method for the PDSI series.
Ensemble forecast with the Transfer Function Model
Once the adequacy of the model is assessed, the model is trained over the period 1900-2014 to produce a simulation plume of annual PDSI for the period 2015-2054. El NiƱo3.4 series and the PDO Series were simulated first, by using the corresponding ARIMA models fitted to the observed time series. Simulations from a  model of the form: