## 4 Results and Discussions
#### Diebold-Mariano Statistical Test  
Table 3 suggests that GRU-1-30 and ARIMA achieved the best results for the RMSE, MAPE, and MAE metrics. As the values of RMSE, MAPE, and MAE are very similar, we used the Diebold-Mariano [50] test to confirm the results. The Diebold-Mariano is a hypothesis test used to compare the significance of differences in two different prediction models. Table 5 presents the results obtained.  
The Diebold-Mariano test result equals zero when the techniques being tested are equal; negative values are present when the left technique obtains a better performance and vice-versa. If the absolute Diebold-Mariano results are high, the tested techniques have significantly different prediction values. The first line of Table 5 shows the comparison between the case site technique compared to all other models.  
It is clear that the existing manual technique used at the case site has the worst performance in comparison to the all models examined. The high statistical values obtained for this technique confirms that it is suboptimal for STLF in this case. The only model that outperformed the ARIMA model was the GRU-1-30 model. All deep-learning models outperformed the machine-learning models. However, the variance in Diebold-Mariano values are not as significant. While the Diebold-Mariano test results for deep-learning models are similar, the GRU-1-30 model achieved the best prediction indexes when compared to all models tested. As such, the initial hypothesis from the grid search results are confirmed.  
These results suggest a significant improvement in the accuracy of the STLF for this energy-intensive manufacturer. This can be used to provide more accurate energy management to  
Figure 11: Daily load forecasting using **(a)** the case site technique and **(b)** the ARIMA model.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **ARIMA** & **RNN-1-30** & **RNN-4-30** & **LSTM-1-30** & **GRU-1-30** & **SWR-0-1-2** & **Random Forest-3-50** & **Random Forest-6-50** & **Random Forest-6-100** \\ \hline Case site & 51.38 & 51.55 & 51.27 & 50.79 & 51.30 & 51.06 & 50.20 & 49.76 & 49.70 \\ technique & - & \(-0.54\) & \(-0.83\) & \(-1.46\) & \(0.45\) & \(-2.96\) & \(-3.36\) & \(-2.95\) & \(-3.18\) \\ ARIMA & - & \(-0.54\) & \(-0.83\) & \(-1.46\) & \(0.45\) & \(-2.96\) & \(-3.36\) & \(-2.95\) & \(-3.18\) \\ RNN-1-30 & - & - & \(-1.39\) & \(-1.34\) & \(1.99\) & \(-2.43\) & \(-2.76\) & \(-2.41\) & \(-2.56\) \\ RNN-4-30 & - & - & - & \(-0.99\) & \(3.04\) & \(-2.07\) & \(-2.57\) & \(-2.25\) & \(-2.40\) \\ LSTM-1-30 & - & - & - & - & \(6.56\) & \(-1.96\) & \(-2.81\) & \(-2.37\) & \(-2.54\) \\ GRU-1-30 & - & - & - & - & - & \(-3.87\) & \(-4.47\) & \(-3.61\) & \(-3.71\) \\ SVR-0-1-linear & - & - & - & - & - & - & \(-0.24\) & \(-0.78\) & \(-1.08\) \\ Random & - & - & - & - & - & - & - & \(-0.76\) & \(-1.15\) \\ Forest-6-50 & - & - & - & - & - & - & - & - & \(-1.83\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Two-sample Diebold-Mariano test results for the deep-learning and machine-learning models and the manual and ARIMA approaches.  
meet production demands, to improve cashflow, to reduce environmental impact, and to mitigate risks associated with energy inefficiencies. Accurate STLF results can be used for anticipatory optimisation and remediation. For example, anomaly detection can be used to identify possible machine degradation or failure from anomalous loads at different stages in the manufacturing process. This would enable predictive maintenance and avoid production downtime.