## 3 Case Study
### Prediction Results and Analysis
#### 3.4.2 Comparison and Analysis of Forecasting Results  
To illustrate the performance of the proposed method, three additional forecasting models including ARIMA model, LSSVM model, and EMD-LSSVM model were used to perform the performance comparison. The processes of the LSSVM model, ARIMA model, and EMD-LSSVM model were similar to the forecasting progress in Section 3.4.1. The evaluation indexes of four different models are shown in Table 2 and the corresponding prediction results are shown in Figure 5. From these comparisons, some main observations are provided below:  
* Compared with the other three involved models, the proposed model had better forecasting performance, where its error indexes of MAE, MRPE, RMSE, RMSRE, and EC were 1.721, 3.969%, 2.974, 6.797%, and 0.9956, respectively. Specifically, in Figure 4, the red line represents the prediction result of the proposed model, while the blue line represents the true value. Their comparison indicates the proposed method could well capture the time-varying characteristics of the actual situation. From Table 2, the forecasting accuracy of the proposed model was higher than the EMD-LSSVM model with the reductions in terms of the five indexes MAE, MRPE, RMSE, RMSRE, and EC by 2.654, 5.991%, 2.831, 8.464%, and 0.0174, respectively. The reason could be that the TVF-EMD algorithm uses time-varying filtering technology, which could describe the time-varying characteristics of the data. Simultaneously, it can improve the imperfection of the model mixing in the EMD algorithm.
* Compared with the single models, the decomposition-based forecasting methods had the higher forecasting accuracy. For example, five error indexes in terms of MAE, MRPE, RMSE, RMSRE, and EC of the LSSVM model were 8.131, 17.871%, 10.801, 27.674%, and 0.9336, respectively, which presents the evident accuracy reduction in comparison with those of the proposed method. Compared with EMD-LSSVM model, these indexes were reduced by 3.756, 7.911%, 4.996, 12.413%, and 0.0306, respectively. The reason for these phenomena could be attributed to high  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & _MAE_ & _MRPE_ & _RMSE_ & _RMSRE_ & _EC_ \\ \hline LSSVM & 8.131 & 17.871\% & 10.801 & 27.674\% & 0.9336 \\ EMD-LSSVM & 4.375 & 9.96\% & 5.805 & 15.261\% & 0.9642 \\ TVF-EMD-LSSVM & 1.721 & 3.969\% & 2.974 & 6.797\% & 0.9816 \\ ARIMA & 8.284 & 17.977\% & 11.01 & 27.25\% & 0.9322 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The comparison results of different methods (A).  
Figure 5: The predictions of different methods (A).  
non-stationarity and nonlinear characteristics embedded in the original data, which could be effectively addressed by the decomposition methods.
* The MAE, MRPE, RMSE, RMSRE, and EC of the ARIMA model were 8.284, 17.977%, 11.01, 27.25% and 0.9322. Compared with LSSVM, these indexes were reduced by 0.153, 0.106%, 0.209 0.424, and 0.0014, respectively. The reason could be attributed to that the nonlinear features hidden in the original data were more significant than those of linear one, which leads to the conclusion that the linear ARIMA model cannot capture the characteristics well. Therefore, it owns the lowest forecasting accuracy.