# Short Term Electric Load Forecasting Based on Data Transformation and Statistical Machine Learning
## 3 Results
The main criterion for the use cases selection was the diversity of the examined datasets. Hence, we test our methodology with different time periods, level/magnitude of demand, consumption patterns and specific characteristics such as demand volatility. By doing so, its applicability is expanded and its advantages are verified. The size of the examined datasets is summarized in Table 3.  
For each dataset, the results of the proposed method are compared with the corresponding results from algorithms which are among the most employed methods across literature. To evaluate the forecasting accuracy, we estimate the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE) [64] as follows:  
\[MAE=\frac{\sum_{i=1}^{n}|A_{t}-F_{t}|}{n},\qquad RMSE=\sqrt{\frac{1}{T}\sum_{t =1}^{T}|A_{t}-F_{t}|} \tag{8}\]  
where \(A_{t}\) are the actuals and \(F_{t}\) the corresponding forecasted values. Another metric that is also very popular across literature is the Mean Absolute Percentage Error (MAPE) [65] which is defined as:  
\[MAPE=\frac{100}{n}\frac{\sum_{i=1}^{n}|A_{t}-F_{t}|}{A_{t}}\gamma_{\text{o}} \tag{9}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Trento** & **Household** & **Office** \\ \hline Size (days) & 9 & 14 & 15 \\ Dataset size (observations) & 1296 & 2016 & 4320 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Datasets Results. MAPE gives a percentage, so it is useful for comparison purposes. Moreover, percentages are in general, more understandable to people and thus MAPE provides initial information regarding the accuracy of the forecasted time series. Like all percentage errors, MAPE has the advantage of being scale-independent hence it is often employed when we need to compare different time series. On the other hand, MAPE as a percentage, has the disadvantage of being undefined or infinite in case of \(A_{t}=0\), or having extreme values when \(A_{t}\) is close to zero. Some software tools ignore actual values that are equal to zero, however this aggravates the aforementioned issue since MAPE cannot take into account the forecasts when the actual value is zero. Another issue with percentage metrics is the assumption that \(A_{t}\) has a scale based on quantity. However, this is not the case with time series like temperature or energy demand since they are not measuring quantity. Moreover, MAPE value can be over 100% or even negative. A MAPE over 100% means that the errors are \"much greater\" than the actual values. Based on the above limitations, MAPE, which is a very common accuracy metric, should be used in conjunction with other metrics in order to have a clear indication and better understanding of the examined forecasting models. Because of the nature of load time series and the shortcomings of MAPE, in order to evaluate the performance of our proposed method, we employed only metrics that are related to the absolute values or squared differences of the examined time series, namely Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). In order to determine the optimal batch sizes for our model, we need to examine the results of the trial and error method applied. The batch sizes examined were multiples of the highest correlated values above. For example for the Trento dataset we experimented with batch sizes of 144, 288 (144 \(\times\) 2), 432 (144 \(\times\) 3), but also with a number of randomly chosen ones like 231 or 216 for the office dataset in order to strengthen our assumption. In Figures 5-7 the achieved values of MAE and RMSE are presented for different batch sizes for the Trento, household and office datasets respectively. Each dataset is split in two parts, namely the training (80%) and the testing (20%) datasets. Those three datasets present the most interesting scenarios, because the availability of data is very limited and the investigated datasets present higher volatility on their consumption patterns, since they are small scale examples.