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.
The histogram and QQ plots of the residuals between the predicted and observed values for the PDSI time series during the validation period show a valid performance of the residuals with an approximate Normal distribution.