# Hierarchical Modelling for CO\({}_{2}\) Variation Prediction for HVAC System Operation
## 6 Results and Discussion
### Parameter Selection  
Under different history and future time windows, this subsection explains the effect of parameters, including the GAF representation method, CNN models and their hyper-parameters, and ensemble learners. To that end, a subset of 10,000 data points for each history and future window combination (h&f) are used for parameter selection. A trial-and-error approach is conducted to find a subset that can balance training and evaluation times and underfitting avoidance. All the combinations of features were evaluated using a Grid Search method. More profound and less time-demanding approaches [50] will be investigated in future work. The sample of 10,000 data points is split into training, validation, and testing sets following the explained experimental procedure. Since many parameters are involved in the parameter selection procedure, this section explains a subset of these experiments. Keen readers and practitioners can refer to the code available through the GitHub repository for a comprehensive overview of the obtained results and the effect of all parameters. As such, the analysis in this section is restricted to the effect of different ensemble learners, the h&f combinations, and CO\({}_{2}\) variation thresholds on the performance of the HMCOVP. Table 2 summarises the findings of the parameter selection grouped by h&f. The best-performing combination of parameters and hyper-parameters with respect to each h&f are highlighted in bold. To highlight the significance of these differences in the MAE, it is important to map the obtained MAE values to their physical representations. The CO\({}_{2}\) variation predictions help the ventilation systems in their decision-making process. Therefore, as previously mentioned, small MAEs can accumulate to falsely trigger the ventilation system. Moreover, less accurate CO\({}_{2}\) variation predictions imply inaccurate prediction of the current effect of occupants and ventilation systems on CO\({}_{2}\) concentration variations. Both of these factors contribute to reflecting an imprecise image of the environment in the HVAC decision-making systems. Accordingly, HVAC systems can be activated either early or late, contributing to potential violations of indoor environmental requirements and an increase in energy expenditure. As such, the MAE reflects a fundamental aspect of the HVAC system operation. The variants of decision trees are the best-performing algorithms, represented by DT and RF. This shows that the non-linearity defines the relationship between the individual learners' predictions and the historical e2s environmental features manifested through the superior MAE of non-linear algorithms (NN, RF, and DT) compared to the RR algorithm. The expansion of the prediction window contributed to a systematic increase in the MAE for all algorithms. This consensus is broken by the RF algorithm such that its MAE value decreases when the prediction horizon increases from 15 to 20 min. However, with more runs to execute, this exception will be reversed to conform to the trend. This increase in MAE is expected with the expansion of the future time window, given the increased probability of uncertainties affecting the environment, including the CO\({}_{2}\) concentrations. In terms of the GAF representation, the best-performing models for each h&f combination do not highlight a preferable method. However, most ensemble learners display a better performance with the local method. Therefore, the CNN models extract representative information of CO