## 2 Literature Review
### Bibliometric Review
This is also confirmed by the seasonal component, shown in Figure 4.

In the seasonal component chart, all the dips to below \(-1.0\times 10^{6}\) MWh occurred either in June or in July when it is winter in Brazil, and all peaks above \(1.0\times 10^{6}\) MWh are registered in March, during the transition from summer (until the 20 th) to autumn. This suggests a correlation between the energy consumption pattern and the temperatures in Brazil. This causality is more deeply studied in Section 4.5. After removing the trend and seasonal patterns, the residual component represents the unexplained variation or noise in the time series data. A sharp drop between April and July 2020 is observed in the residual component, potentially linked to the COVID-19 pandemic, officially declared by the World Health Organization on 11 March. This period may have decreased energy consumption due to pandemic-related restrictions and changes in societal behavior, as found by [60]. This also appears to be responsible for the drop in the trend component in 2020. ### Long-Term Memory Test

The capacity of a time series to retain patterns over extended periods refers to its long-term memory. It reflects the degree to which past observations influence future observations in the series. It indicates how well the historical data of the time series are preserved or remembered over time. Comprehending the long-term memory of a time series is fundamental for revealing its underlying dynamics, analyzing trends, identifying patterns, and improving the reliability of forecasts based on historical data. In this regard, a time series is said to have persistent behavior if it tends to replicate its patterns over time, manifested as momentum in the data, whether characterized by increasing or decreasing trends. This means that increases follow increases in values, and decreases in values are followed by decreases in values. Conversely, an anti-persistent time series is more likely to experience an increase in value after a decrease and vice versa. This creates a mean reversion behavior rather than continuing in the same direction. A time series may also present a Brownian motion behavior in which future values do not depend on past observations. This poses a challenge to time series forecasting. The Hurst exponent (\(H\)) evaluates a time series regarding their long-term memory. This metric, \(H\in[0,1]\), indicates whether a time series presents a persistent (\(H>\) 0.5), anti-persistent (\(H<\) 0.5), or random (\(H=\) 0.5) behavior. The variation of the Hurst Exponent over a 100-month wide window is calculated for the energy consumption time series and its residual and trend components. This analysis does not include the seasonal component due to its evident cyclical behavior. The results are presented in Figure 5, demonstrating that energy consumption in Brazil has a consistent growth trend despite the inflection points, such as the one possibly caused by the COVID-19 pandemic. In contrast, the energy consumption time series and its residual components follow an anti-persistent behavior. The persistent behavior of the trend component, along with the

Figure 4: Decomposition of the time series into the trend, seasonal, and residual components. fact that no Brownian motion behavior (\(H=0.5\)) (red dashed lined in Figure 5) is observed, implies that Brazil's energy consumption is predictable by observing its past values. ### Interaction with Exogenous Variables

Understanding the intricate relationship between energy usage and external factors is essential to gain a comprehensive perception of the dynamics of energy demand. Economic fluctuations, for example, may impact energy consumption trends, reflecting shifts in production, consumption patterns, and overall economic activity. Similarly, climatic variables, such as temperature and precipitation, may influence energy demand, particularly in sectors like heating and cooling.