Figure 11. The ARCH/ARMAX model predictions with and without the CO2 estimated effects and the actual temperature outcomes, 1 Jan 2016 – 31 Aug 2017.
The structural predictions are less accurate than the predictions from the full model but may yield useful insights. The predictions from the structural model have an RMSE equal to 5.21 oC while constraining the CO2 estimated effects to be equal to zero results in predictions with an RMSE equal to 8.29oC (Figure 12). In short, constraining the estimated effects of CO2 to be equal to zero reduces the structural model’s predictive accuracy. In terms of temperature, the predicted level is significantly lower when the estimated structural effects of CO2 are ignored (Figure 13). Observe that the difference in the mean levels of predicted temperature is nontrivial.