# Prophet-CEEMDAN-ARBiLSTM-Based Model for Short-Term Load Forecasting
## 3 Experiment Results and Analysis
### Comparison with Other Existing Models  
The paper compares the forecasting values with the existing methods, validating the forecasting accuracy of the models. Simultaneously, the sliding window t is set to 24 for predicting the load of the next 24 h, and the resulting curve of the models is depicted in Figure 9. It can be observed from Figure 9 that the MAE values of ARIMA and ETS are higher than other benchmark models at most time points. This shows that the above models can only capture the overall trend of load change in one day, and they cannot identify the fine change in load series. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **MAPE (\%)** & **MAE (Mwh)** & **RMSE (Mwh)** \\ \hline Prophet-CEEMDAN-Dense & 5.49 & 812.68 & 1091.77 \\ Prophet-ARBiLSTM & 3.00 & 450.85 & 655.88 \\ CEEMDAN-ARBiLSTM & 2.37 & 346.92 & 474.52 \\ Prophet-CEEMDAN-ARBiLSTM & 1.66 & 234.57 & 330.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Effectiveness validation of the modules on the test set. Figure 8: The losses of the Prophet-ARBiLSTM, the CEEMDAN-ARBiLSTM, the Prophet-CEEMDAN-Dense, and the Prophet-CEEMDAN-ARBiLSTM. The MAE values of Prophet-LSTM and Prophet-GRU are close at most time points. It demonstrates that the Prophet-LSTM can effectively leverage the historical electricity load data to forecast future load values, yielding an accurate forecasted result. However, the LSTM method cannot accurately fit the volatile load data, leading to the reduction in the forecasting accuracy. The Prophet-GRU can enhance the performance of the electricity load. Nevertheless, it struggles to precisely capture the random features of the load data, limiting the forecasting performance. The Prophet-EEMD-LSTM model employs EEMD to mitigate uncertainty in electricity load data, but there is room for improvement in extracting random load features. It can be observed from Figure 9 that the MAE values of Prophet-CEEMDAN-ARBiLSTM are lower than those of Prophet-EEMD-LSTM at most time points. It shows that the Prophet-CEEMDAN-ARBiLSTM adopts the CEEMDAN method to decompose the uncertain input data, effectively forecasting the uncertain changing trends. Moreover, the ARBiLSTM block extracts temporal features influencing load variations from the input series. Consequently, Prophet-CEEMDAN-ARBiLSTM produces accurate forecasting results. The proposed method is compared with Prophet-LSTM, Prophet-GRU, and Prophet-EEMD-LSTM to validate the performance of Prophet-CEEMDAN-ARBiLSTM, as presented in Table 2. It can be seen that the most superior accuracy is found with the Prophet-CEEMDAN-ARBiLSTM model. Compared to Prophet-EEMD-LSTM, the performance metrics show a reduction of 0.26% in MAPE, a decrease of 48.94 in MAE, and a decrease of 79.76 in RMSE. Compared to Prophet-LSTM, the reductions are 1.61% in MAPE, 258.45 in MAE, and 375.58 in RMSE. Compared to Prophet-GRU, the reductions are 1.57% in MAPE, 254.23 in MAE, and 370.6 in RMSE. These results indicate that Prophet-CEEMDAN-ARBiLSTM effectively leverages the strengths of Prophet, CEEMDAN, and ARBiLSTM, thereby promoting generalization ability. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **MAPE (\%)** & **MAE (Mwh)** & **RMSE (Mwh)** \\ \hline ARIMA & 7.73 & 1138.59 & 1364.69 \\ ETS & 5.47 & 814.56 & 1095.98 \\ Prophet-LSTM & 3.27 & 493.02 & 706.53 \\ Prophet-GRU & 3.23 & 488.8 & 701.55 \\ Prophet-EEMD-LSTM & 1.92 & 283.51 & 410.71 \\ Prophet-CEEMDAN-ARBiLSTM & 1.66 & 234.57 & 330.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison of the different methods. Figure 9: Forecast error comparison of the methods in one year. Figure 10 illustrates the MAE comparison for the models across different seasons. It can be observed from Figure 10a that each model possesses a large MAE from 5 a.m. to 7 a.m. However, the MAE values of the proposed method and Prophet-EEMD-LSTM are significantly lower than those of other benchmark models.