## 3 Dataset and Evaluation
### Evaluation  
The DCF algorithm was assessed for short- and long-term forecasting. The short-term forecasts for 1-, 2- and 3-hour ahead were generated, as is common in the literature [12; 29; 36; 37]. Forecasts for a few hours ahead help to manage and schedule the start-up of power plants (load scheduling) [37]. Furthermore, short-term forecasts of 30 min to 6 h are important for load dispatch and scheduling [24]. Load dispatch means that electricity can be dispatched on demand, and load scheduling is the management of this electricity and its usage.  
The long-term prediction capabilities were investigated by forecasting irradiance data for 1 year (24 \(\times\) 365 h) ahead. Long-term forecasting of several months up to a year is useful for scheduling maintenance and has value when bidding on the energy market [38]. There are few studies on long-term predictions in the literature using statistical methods [12]. It might relate to the fact that physical models based on meteorological expertise are generally more accurate at predicting long-term solar radiation [39]. The long-term prediction of this ML model does not detect any change in weather and only gives an approximate idea of the radiation values. However, this model is useful, as its implementation is easier and quicker than the implementation of a physical model and still gives a good indication of the amount of radiation that will be received  
All models were tested on hourly data for a whole year (2005). These results were affirmed using fivefold cross validation for the SVM model. Cross validation for FBP cannot be performed like common k-fold validation, as the time series should not be randomly separated. Therefore, the 1-, 2-, and 3-hour predictions were made for FBP using every  
Figure 2: The 1D and 2D representations of average irradiance in Boston and Denver [34]. **(a)** 1D representation of average irradiance in Boston **(b)** 1D representation of average irradiance in Denver **(c)** 2D representation of average irradiance in Boston **(d)** 2D representation of average irradiance in Denver.  
hour of the year as the starting point, thus generating 8760 \(\times\) 3 forecasts. Based on these predictions and target values, several evaluation metrics were calculated. As for k-fold cross validation, the more starting points there are (the higher the k), the more generalised the result will be.  
The forecasting was evaluated and compared using the coefficient of determination (R\({}^{2}\)), mean absolute error (MAE), and root-mean-squared error (RMSE).  
The R\({}^{2}\) value is obtained as follows [40]:  
\[R^{2}=\frac{\Sigma_{i}(y_{i}-\hat{y}_{i})}{\Sigma_{i}(y_{i}-\overline{y}_{i})} \tag{2}\]  
where \(y_{i}\) are the actual values, \(\overline{y}_{i}\) is the mean of the actual values, and \(\hat{y}_{i}\) are the predicted values.  
MAE has the same units as the predicted value and thus represents the expected absolute error, which is calculated by [41].  
\[MAE=\frac{1}{N}\ \sum_{i=1}^{N}\lvert y_{i}-\hat{y}_{i}\rvert \tag{3}\]  
where \(N\) is the total number of samples.  
The RMSE value squares the difference between actual and predicted values, emphasising larger errors. This is appropriate for solar prediction as larger errors lead to disproportionally higher costs [42]. RMSE can be calculated as follows [43]:  
\[RMSE=\sqrt{\sum_{i=1}^{N}\frac{(y_{i}-\hat{y}_{i})^{2}}{N}} \tag{4}\]  
To evaluate the prediction accuracy, the data were trained on radiation data from 1998 to 2004 and tested on data from 2005. Cross validation was performed, showing that the models generalise well. Furthermore, grid search was applied to tune the hyperparameters. After training and making predictions, these were adjusted using contextual optimisation.