## 4 Evaluation Criteria  
Various criteria are used in the literature to evaluate the accuracy of load forecasting methods. Researchers have used various statistical metrics, with an emerging focus on probabilistic load forecasting metrics. Table 4 shows the most commonly used statistical measures in the field. Here, \(n\) denotes the sample size, \(x^{\prime}_{i}\) denotes the model's predicted value, and \(x_{i}\) denotes the actual value. The second-degree loss function provided by RMSE prioritizes larger errors over smaller ones. Mean average error (MAE) is naturally measurable and is unambiguous. Mean average percentage error (MAPE) can be easily applied to both large-volume and small-volume items and is not scale dependent. However, differential error often leads to biased predictions. In typical load forecasting problems, demand at the aggregate level rarely approaches zero or is very small, so the shortcomings of MAPE, such as problems with handling small and zero denominators, are not very significant [38]. When the error distribution is anticipated to be Gaussian, reference [65] asserted that the root mean square error (RMSE) is more appropriate than the MAE; however, although this would help to elicit more information from the data, it is often ignored in the reviewed articles. According to the objective of the research, the following additional variables were found in the literature:  
* The largest negative and positive differences between a predicted value and the actual values are indicated by the terms maximum negative error (MNE) and maximum positive error (MPE), respectively. For some applications, these values may be more relevant than the typical error (e.g., fuel storage forecasting in a power plant). * Relative root mean square error (rRMSE) normalizes the RMSE by dividing it by the range of actual values. This makes it easier to compare prediction accuracy across datasets of different scales. * The coefficient of determination (R\({}^{2}\)), which is used in the literature to measure the fit of the prediction model [66]. If R\({}^{2}\) is closer to 0, this indicates low predictive ability and poor fit of the data. * Percentage error (PE) quantifies the relative discrepancy between forecasted and actual values, expressed as a percentage. It provides clarity on the direction and extent of forecast inaccuracies. * The residual sum of squares (RSS), which represents the expected deviations from actual data values, is the sum of the squares of the residuals. It can be calculated using the RMSE. It measures how much divergence there is between the actual data and an estimated model. * Pearson's correlation coefficient (Pearson's \(r\)) measures the linear relationship between forecasted and actual values. A high correlation indicates a robust linear relationship, indicating that the forecasting models are effectively capturing the underlying patterns. * The standard deviation of residuals is a statistical term used to represent the difference between the standard deviations of the observed values and the anticipated values, as indicated by the points in a regression analysis. \begin{table}
\begin{tabular}{c c} \hline \hline
**Criterion Name** & **Formula** \\ \hline Mean Absolute Error (MAE) & \\ Root Mean Square Error (RMSE) & \\ Mean Average Percentage Error (MAPE) & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Formulas for Evaluation Criteria. * Bias quantifies the consistent deviation of forecasts from actual values. Positive bias indicates consistently higher forecasts, while negative bias indicates consistently lower forecasts. * Some authors also employ quality comparisons between the time series generated by different algorithms and the real validation data [67]. Calculating these variables makes it easier to compare the results of different methods, especially by evaluating models that share identical influential factors and datasets. However, such a simple study may not be very informative, particularly when there is small variation between the methods or the dataset is not very large.