## 2 Literature Review
### Bibliometric Review
Figure 7 shows that the dry bulb temperature and the seasonal component of the energy consumption have a strong positive correlation, suggesting that the greater the temperature, the higher the energy demand. Figure 2:2 Pearson correlation coefficients between variables, selected according to Granger causality. A strong correlation between the trend component and the economic and industrial factors is noted despite no Granger causality being observed between them. This phenomenon may be attributed to several plausible explanations. Firstly, a common cause could form the basis of the observed correlation, whereby alterations in these factors occur concurrently without direct causal links among them. Alternatively, the potential presence of Granger causality, albeit with a lag greater than three months, was used in the experiment. #### 4.5.3 Cointegration

Cointegration describes the long-term equilibrium relationship between two-time series. Cointegrated series move together in the long run despite exhibiting short-term deviations from their equilibrium relationship. For this analysis, we selected the variables that were found to be Granger causes of energy consumption in Brazil, according to Section 4.5.1. The cointegration between them was assessed with the Engle-Granger test. This test involves regressing one non-stationary variable on another and then testing the stationarity of the residuals obtained from the regression, using the Augmented Dickey-Fuller test. If the \(p\)-value from the unit root test is below 0.05, it indicates that the residuals are stationary, suggesting that the variables are cointegrated. However, if the \(p\)-value exceeds this significance level of 0.05, the null hypothesis of non-stationarity in the residuals cannot be rejected, implying that there is no cointegration between the variables. Figure 8 shows the matrix of cointegration between the selected Granger variables and is presented as the True cointegration if the \(p\)-value is less than 0.05 and as false otherwise. All variables depicted in Figure 8 exhibit Granger causality with energy consumption, but only dew point temperature and relative humidity of air demonstrate cointegration with the energy consumption time series or its components. This suggests a predictive relationship between the two variables, but it may not be a stable long-term relationship. ## 5 Time Series Models

Having conducted the data analysis in Section 4, the patterns, trends, and correlations within the time series are now comprehended, providing meaningful observations of the historical behavior of energy consumption. This knowledge also enables a better configuration of the prediction models, resulting in more accurate values. Figure 2:3 Cointegration between variables selected according to Granger causality. ### Training Settings

The forecast is conducted using the SARIMA, FB Prophet, Holt-Winters, and TBATS models, configured to consider energy consumption's yearly seasonality. These models were selected due to their support for seasonal time series and their previous successful use, as seen in Section 2. The experiment is conducted using Python, version 3.10.12. The libraries used for each model and their training parameters are presented in Figure 2:4 These parameters were selected according to the data analysis discussed in Section 4, with a corresponding reference in Table 4, indicating where the determination of each parameter is elaborated. The parameters not mentioned in Table 4 were set to their default values. It is noted that FB Prophet is easier to use, as it automatically identifies the adequate parameters. Conversely, SARIMA requires manual configuration of several variables. The 24 most recent months (December 2021 up to November 2023) of the data are used to test the predicted values, leaving 215 months available for training.