# Prediction of Intraday Electricity Supply Curves
## 4 Results  
### Error Metrics  
We now present the error metrics for the seven considered models. Tables 3-9 show the summary statistics of the prediction error using the \(d_{K}\) measure. We see that the MLP and CNN models (Tables 4 and 5, respectively) generally obtain good results when compared to the naive model (Table 3). This is not only observed in the centrality measures (mean and median) but also in the dispersion measures (SD and MAD). This is relevant because it implies that the errors with MLP and CNN are smaller and also more concentrated. LSTM-type models, i.e., LSTM, BiLSTM, and CNN+LSTM, do not perform well since their mean and median values are generally much higher than those obtained using the naive procedure. The Transformer model (Table 9) has mixed behavior. We now group the mean prediction errors using the \(d_{K}\) distance to facilitate the comparison of the models. In Table 10, the top three models for each market are colored red, green, and blue. We see that the CNN model obtains the best results in the first five sessions and is the second best in the sixth. In the sixth session, the best model is MLP, although the difference with CNN is small. We also see that the Naive model obtains good results, which indicates that, despite its simplicity, it is a good benchmark. It can be seen that the naive method is the second best in the first session market, only surpassed by the CNN procedure. The Transformer model improves the naive model in the fourth and fifth sessions. Clearly, the best results are obtained for the second to sixth sessions using the MLP and CNN models. The percentage reduction in the error means with the MLP model compared to the naive procedure is between 22.6% in the third session and 63.8% in the fifth session. The reductions with the CNN model are between 35.2% and 69.6% in those sessions. In the fourth and fifth sessions, where the Transformer model is better than the naive procedure, the reductions are 4.0% and 18.6%, respectively. Therefore, they are lower than with MLP and CNN. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Market** & **Mean** & **Median** & **SD** & **MAD** \\ \hline
1 st & 9,949,320 & 7,113,820 & 8,181,740 & 3,309,050 \\
2 nd & 1,335,310 & 509,853 & 1,676,470 & 243,729 \\
3 rd & 396,317 & 368,620 & 163,949 & 80,360 \\
4 th & 363,259 & 346,863 & 189,974 & 95,969 \\
5 th & 318,561 & 298,485 & 156,222 & 78,313 \\
6 th & 4,114,860 & 3,600,920 & 2,997,620 & 1,386,870 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary statistics of the prediction error with the BiLSTM model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Market** & **Mean** & **Median** & **SD** & **MAD** \\ \hline
1 st & 202,487 & 157,074 & 146,240 & 47,723 \\
2 nd & 236,436 & 192,165 & 168,999 & 74,396 \\
3 rd & 203,799 & 164,773 & 146,345 & 55,942 \\
4 th & 182,406 & 146,881 & 132,737 & 55,306 \\
5 th & 161,450 & 129,051 & 116,126 & 43,136 \\
6 th & 143,626 & 120,655 & 98,667 & 41,839 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Summary statistics of the prediction error with the Transformer Model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Market** & **Mean** & **Median** & **SD** & **MAD** \\ \hline
1 st & 201,487 & 157,074 & 146,240 & 47,723 \\
2 nd & 236,436 & 192,165 & 168,999 & 74,396 \\
3 rd & 203,799 & 164,773 & 146,345 & 55,942 \\
4 th & 182,406 & 146,881 & 132,737 & 55,306 \\
5 th & 161,450 & 129,051 & 116,126 & 43,136 \\
6 th & 143,626 & 120,655 & 98,667 & 41,839 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of the mean prediction errors using the \(d_{K}\) measure.