## 2 Materials and Methods
### Input Data Employed for the 24-Hour-Ahead Forecasting  
Our investigations were based on the processing of the measured hourly electrical load during the years from 2017 to 2021, for which the hourly load demand input data for the Greek system were obtained from ENTSO-E [35]. Testing and validation of the models were carried out for various months in 2022. In addition to the electric load curves, meteorological data, at least on a daily basis, need to be employed for representative climatic conditions of Greece. The central location of Athens in Greek geography, and the presence of about 40% of the population and a significant part of industrial and business activity here, allows us to consider Athens weather data as corresponding--more or less--to the average Greek climate as weighted by the number of inhabited space and number of inhabitants. For this purpose, out of the four weather stations of the central Athens area (Gazi, Ambelokipi, Patsisia, Psychico) [36], the suburb of Psychico was selected for weather data [37]. Psychico may be considered as representing the climatic conditions of Athens, which hosts a major part of the population and economic activity, and, on the other hand, its climate is not severely affected by the city-center conditions. On the other hand, because it may be considered to belong to the northern suburbs, and it is not densely built with high-rise buildings, and it has plenty of trees and park space, its climate is not affected by Athens center conditions, a fact that allows it to be more representative of Greece. For this reason, input weather data as daily averages and high-low temperature values were obtained from the meteorological station of Psychico [37]. Apart from meteorological variables such as dry bulb temperature and relative humidity, load presents a high correlation to its past values [4]. To this end, it is interesting to confirm, to the specific dataset, the generally observed short-term periodicity of the load using the Pearson correlation coefficient [38]. In Figure 8, the Pearson correlation coefficients of the current hourly load for the full year 2021, correlated with its previous hourly values up to 216 h before, are graphically presented. Obviously, they start from the value of 1 at zero delay, and they are seen to fluctuate with 24 h periodicity. However, a high correlation coefficient of 0.9344 is clearly observable for a 24 h delay. Next, a higher correlation coefficient  
For the day-ahead load forecast, the following are input parameters usually applied in the specialized literature:  
* Dry bulb temperature;
* Dew point temperature;
* Hour of day;
* Day of the week;
* Holiday/weekend indicator (0 or 1);
* Previous 24 h average load;
* 24 h (previous day) lagged load;
* 168 h (previous week) lagged load. The ambient dry-bub (DB) temperature is included in most investigations because temperature affects electricity consumption. The correlation between the total daily electricity demand (GWh) of the Greek system in 2021 and daily average temperature is shown in Figure 9. A nonlinear relationship between load and temperature is observed. There exists a baseline daily demand of the order of 100-130 GWh, during the days with normal average temperature (DB) in the range 18-24 \({}^{\circ}\)C. With the onset of higher average temperatures, the total daily load steeply increases up to 210 GWh. The same trend is observed when the mean daily temperature deviates to values lower than normal. However, as seen in Figure 9, the effect of lower mean daily temperature levels on the total daily load (GWh) is significantly less pronounced. This is due to the fact that space cooling is carried out almost exclusively by means of electrically driven heat pumps and air-conditioning equipment, whereas the heating is mainly carried out by natural gas, oil and pellet-fueled boilers, and--to a lesser extent--by heat pumps or split units in heating mode. Hourly temperature data (dry bulb and dew point) for locations in high-demand areas of the system are usually considered.