## 2 Literature Review
### Bibliometric Review
In this section, however, we incorporate exogenous variables that exhibit a Granger causality relationship with the energy consumption time series, as seen in Section 4.5. As the Holt-Winters and the TBATS models do not natively support exogenous variables, they are excluded from the analysis of this section. Also, SARIMAX is used, along with FB Prophet, instead of SARIMA. As a consequence, these models are evaluated regarding their accuracy, measured by the MAPE, when adding the exogenous variables of oil production (industrial); GDP, NCPI, and ENCPI (economic) [66]; total precipitation, air temperature, dew point temperature, relative humidity of air and wind speed (climatic). We also assess the accuracy when including all these factors concurrently in the models. The results are shown in Figure 12 for SARIMAX and Figure 13 for FB Prophet. It is worth noting that SARIMAX demonstrated improved optimal accuracy, in comparison to SARIMA, when incorporating exogenous variables in both the original and smoothed time series. Specifically, the original time series, utilizing solely climatic variables, achieved a MAPE of 1.28% with a training window size of 215 months. Conversely, the smoothed time series, incorporating economic variables, returned an even lower MAPE of 1.18% with a training window size of 180 months. In contrast, when considering only endogenous time series data, the MAPE values were slightly higher, at 1.38% for a training window size of 72 months and 1.44% for a window size of 180 months, respectively. Figure 11: Comparison between the actual energy consumption and forecasting univariate models in their optimal training window sizes, according to Figure 10. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Smoothing** & **Metric** & **SARIMA** & **FB Prophet** & **Holt-Winters** & **TBATS** \\ \hline \multirow{4}{*}{No} & MAPE (\%) & 1.38 & 1.91 & 3.85 & 4.17 \\  & MPE (\%) & \(-0.53\) & \(-1.72\) & 3.82 & 4.17 \\  & RMSE (MWh) & \(8.68\times 10^{5}\) & \(1.07\times 10^{6}\) & \(2.03\times 10^{6}\) & \(2.13\times 10^{6}\) \\  & NRMSE\_minmax & 0.15 & 0.19 & 0.37 & 0.39 \\ \hline \multirow{4}{*}{Yes} & MAPE (\%) & 1.44 & 0.71 & 2.53 & 1.44 \\  & MPE (\%) & \(-1.30\) & \(-0.03\) & 2.50 & 1.44 \\  & RMSE (MWh) & \(6.87\times 10^{5}\) & \(3.99\times 10^{5}\) & \(1.37\times 10^{6}\) & \(7.81\times 10^{5}\) \\  & NRMSE\_minmax & 0.23 & 0.13 & 0.46 & 0.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of MAPE, MPE, RMSE, and NRMSE_minmax between the univariate models in their optimal conditions, according to Figure 10.

In the case of the FB Prophet model, an interesting observation emerges. Contrary to expectations, including economic exogenous variables seems to have a detrimental effect on model accuracy. When considered in isolation, these variables resulted in a maximum Mean Absolute Percentage Error (MAPE) of 42.08%, and when combined with industrial and climatic factors, the MAPE increased to 52.79%. Interestingly, while incorporating exogenous variables did not significantly enhance the model's accuracy in the smoothed time series, it marginally improved accuracy in the original version. Specifically, accuracy improved from 1.91% with endogenous variables alone to 1.62% with a training window of 144 months, considering industrial variables. None of the models incorporating all factors simultaneously produced superior results. However, when each category of exogenous variables was considered independently, the best accuracy was achieved under specific scenarios. Industrial variables enhanced the accuracy of the smoothed time series in the Facebook Prophet model, while climatic variables benefited the original time series in SARIMAX. Economic variables, conversely, demonstrated a modest improvement in accuracy for the smoothed version in SARIMAX. The original time series in the Facebook Prophet model generated the best results when considering endogenous variables exclusively.