# Predicting the Gap in the Day-Ahead and Real-Time Market Prices Leveraging Exogenous Weather Data
## 5 Simulation Results
### Performance Evaluation  
To understand the quantitative insights for the DAM, RTM, and gap prices, the descriptive statistics of the entire data set are presented in Table 3, where all the values are in USD/MWh. It is worth pointing out that the standard deviation for the DAM was almost half of that for the RTM, which means that the values tend to be closer to the mean in the case of the DAM and prices do not fluctuate as much as the price fluctuations in the case of the RTM. The 25 th percentile of all gap prices is less than \(-0.16\), which means that almost a quarter of the direct gap prices are negative. Figure 4: A comparison between the probability distribution of direct gap predictions and the difference between separately predicted prices for the DAM and RTM at 5 pm, procured by LSTM network. Figure 3: A comparison between the probability distribution of direct gap predictions and the difference between separately predicted prices for the DAM and RTM at 8 a.m., procured by LSTM network. In Tables 4 and 5, an evaluation of the DAM prices and RTM prices procured by the learning methods presented in Section 2 is illustrated, where the unit for the MAE, RMSE, and max error is USD/MWh. All algorithms performed significantly better at predicting DAM prices than predicting RTM electricity prices. For instance, the LSTM network, which is the best-performing algorithm, had an MAE and RMSE of 4.9 and 7.1, respectively, while, for the RTM, the same algorithm resulted in a MAE of 21.2 and an RMSE of 48. Consequently, the complexity of predicting the gap between these markets is dependent on the accuracy of the prediction of the RTM. LASSO failed to capture any spikes in the price change, and the maximum error between the prediction and the actual gap values was 1054.8 USD/MWh. The poor performance of the LASSO algorithm can be explained by the fact that LASSO is a linear algorithm and leverages a linear function for prediction, while gap prediction should be a non-linear mapping based on empirical evidence. The most promising results were procured using the RF algorithm and the LSTM network. The Random Forest algorithm had an MAE score of 24.5 USD/MWh and an RMSE score of 67.5 USD/MWh when predicting direct gap prices. Even though these metrics are slightly worse than the above-described algorithms, it can be observed from Figure 5 that the RF algorithm is not as good as the LSTM network. While the RF does a good job of predicting correct values when predicting positive gap prices, it suffers from a notable error in capturing a big negative price spike in gap values. The LSTM network had the best performance in terms of error metrics as well as an empirical evaluation based on the plot provided in Figure 5. Furthermore, Figure 6 illustrates the relative error of the price gap predicted by the LSTM and RF methods. Table 6 shows that the LSTM network \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Error Measure** & **LASSO** & **SVR** & **RF** & **LSTM** \\ \hline MAE & 9.6 & 11.7 & 5.1 & 4.9 \\ \hline RMSE & 13.3 & 33.7 & 7.9 & 7.1 \\ \hline nRMSE [\%] & 7.4 & 39.8 & 4.4 & 4.2 \\ \hline Max Error & 95.2 & 122.7 & 62 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Prediction errors for the DAM. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Statistics** & **Gap** & **DAM** & **RTM** \\ \hline Mean & 3.1 & 39.1 & 36.0 \\ \hline Standard Deviation & 87.7 & 45.6 & 84.5 \\ \hline Min & \(-1488.6\) & \(-61.6\) & \(-262.3\) \\ \hline Max & 2276.2 & 2374.4 & 1545.4 \\ \hline
25 th Percentile & \(-0.16\) & 25.0 & 19.6 \\ \hline
50 th Percentile & 6.6 & 33.4 & 27.1 \\ \hline
75 th Percentile & 17.5 & 46.5 & 36.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical analysis of DAM, RTM, and gap prices of the data set.