## 2 Literature Review
### Bibliometric Review
By leveraging exogenous variables in the analyses, not only is the understanding of the factors that shape energy consumption patterns enhanced, but forecasting models may also improve in accuracy. This possibly enables these variables to serve as valuable indicators of external influences that drive changes in energy demand, allowing us to anticipate and adapt to evolving dynamics in the energy landscape. By meticulously analyzing these interactions, we aim to improve comprehension that facilitates informed decision-making in energy planning, resource allocation, and policy formulation. #### 4.5.1 Granger Causality

Granger causality determines whether one time series can be used to predict another time series [61]. It asserts that a given time series, denoted here as X, Granger-causes (or G-causes) another time series, designated as Y, under the condition that the historical data of X contribute to a superior forecasting accuracy of Y compared to relying solely on Y's past data. The hypotheses of the test are as follows:

**Hypothesis 5**. : _The lagged X-values do not explain the variations in Y, i.e., X(t) does not G-cause Y(t)._

**Hypothesis 6**. : _The lagged X-values may explain the variation in Y, i.e., X(t) G-causes Y(t)._

For each pair of variables in our dataset, the Granger causality is tested for a maximum lag of three months, and the causality is only considered valid if the null hypothesis is rejected for all three lags. Figure 6 displays the results, in which the rows represent the causes being tested and the columns are the targeted time series. Figure 2:0 Variation of the Hurst exponent along the energy consumption time series and its components. Figure 2:1 Grange causality results between energy consumption and different factors. It is important to note, however, the Granger causality does not imply a symmetric relationship between two variables; that is, (X(t) \(\rightarrow\) Y(t)) \(\implies\) (Y(t) \(\rightarrow\) X(t)), in which the \(\rightarrow\) represents the Granger causality. Because of that, the matrices in Figure 6 are not symmetrical concerning their main diagonal. Also, one variable cannot G-cause itself; therefore, the matrices are also false in their main diagonal. While oil production was the only industrial factor to Granger-cause energy consumption (Figure 6a), the climatic factors were the main ones responsible for the seasonal component of the energy usage (Figure 6b). The Granger causality testing, however, does not provide information about the direction of the causal effect between variables. That is, it cannot determine whether the energy consumption rises or falls after an increase in the temperature. Section 4.5.2 assesses the relationship between these variables' directions. Figure 6c shows that the economic indexes do not G-cause the trend or seasonality. However, the GDP, NCPI, ENCPI, and uni-direction Granger causality influence Brazil's energy consumption (EC) time series. This finding diverges from those found by [62], which stated the causality in the reverse order between 1963 and 1993; that is, EC \(\rightarrow\) GDP. The Granger causality between economic growth and energy consumption has been studied in several countries, such as Italy, as conducted by [63] and in G7 countries, as conducted by [64]. It has been observed that, for example, between 1990 and 2014, EC \(\leftrightarrow\) GDP globally, while EU countries had EC \(\rightarrow\) GDP, and, between 1960 and 2012, Belgium had GDP \(\rightarrow\) EC, according to [65], as our current findings for Brazil. #### 4.5.2 Correlation

The assessment of the correlation between variables enlightens the direction of the relationship between variables and causality relationship. For this analysis, we have selected exclusively the variables that demonstrated, in Section 4.5.1, Granger causality to energy consumption or any of its components. The correlation confirms the observations from Section 4.3.1, which concluded that the energy consumption was higher in the Brazilian summer.