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.