## 2 Knowledge and Tools of Model Preparation
MPI represents the average width of the obtained interval. AWD is the accumulated width deviation of testing dataset, which could be obtained by calculating the relative deviation degree. The cumulative sum of AWD\({}_{i}\) can measure the relative deviation degree. See Table 4 for the specific description of the formula. ### Diebold-Mariano Test

To verify the designed hybrid model owns better forecasting ability than compared models, an effective verification method called Diebold-Mariano (DM) test proposed by Diebold FX and [PERSON] is adopted. The theory of DM test is introduced first. Considering the significance level \(\alpha\), zero hypothesis H\({}_{0}\) indicates the predictive effectiveness of the developed model and the comparison model are not significantly different. The meaning of H\({}_{1}\) is contrasted with H\({}_{0}\). The relevant formulas are shown as:

\[\mathrm{H}_{0}:\mathbf{E}[\mathbf{L}(\mathbf{err}_{i}^{1})]=\mathbf{E}[\mathbf{L}(\mathbf{err}_{i}^{2 })] \tag{20}\]

\[\mathrm{H}_{1}:\mathbf{E}[\mathbf{L}(\mathbf{err}_{i}^{1})]\
eq\mathbf{E}[\mathbf{L}(\mathbf{err}_{i }^{2})] \tag{21}\]

In the formula, \(L\) represents the loss function of prediction error. \(\mathbf{err}_{i}^{1}\) and \(\mathbf{err}_{i}^{2}\) are the error sequence predicted by selected model. In addition, the statistics of DM test can be defined in the following ways:

\[\mathrm{DM}=\frac{\sum_{i=1}^{n}\left(\mathbf{L}(\mathbf{err}_{i}^{1})-\mathbf{L}(\mathbf{err }_{i}^{2})\right)}{\sqrt{S^{2}/n}}s^{2} \tag{22}\]

in which \(S^{2}\) is the estimate of the variance of \(d_{i}=\mathbf{L}(\mathbf{err}_{i}^{1})-\mathbf{L}(\mathbf{err}_{i}^{2})\). Assuming a certain significance level \(\alpha\), the obtained value DM is in comparison with that of \(z_{\alpha/2}\). Once DM statistics exceed the interval \([-z_{\alpha/2}z_{\alpha/2}]\), H\({}_{0}\) can be rejected. This shows the predictive performance of the established model and that of the comparative model are significantly different, which means that H\({}_{1}\) will be accepted. ### Results and Analysis of Point Forecasting

To testify the performance of the point prediction module, two experiments are conducted in this part: experiment I and experiment II. The main purpose of experiment I is to prove the good ability of the nonlinear combination model in the point forecasting, so as to reasonably verify the superiority of the proposed model. In addition, experiment I proves the necessity of data preprocessing. In the same way, to prove the rationality and superiority of the ICEEMDAN technology selected in this work, it is compared with other commonly used data preprocessing technology, and this is the content of experiment II. The detailed analysis of each experiment is as follows. #### 4.4.1 Experiment I: Comparison with Individual Models

In this work, all experimental datasets are trialed to assess the effectiveness of the point prediction module, while three comparisons are designed. In comparison (a), the proposed model is compared with the four data preprocessed models, ICEEMDAN-RBF, ICEEMDAN-ELM, ICEEMDAN-ENN and ICEEMDAN-ARIMA, in order to analyze the advantages of the combination model using the nonlinear combination method. In comparison (b), four ICEEMDAN-based models are compared with single models RBF, ELM, ENN and ARIMA, respectively. In comparison (c), the effectiveness of the designed forecasting model is further tested by using the traditional model SVR and Generalized Regression Neural Network (GRNN) as comparison methods. The predicted results are displayed in Table 5 and Figure 4, and the comparison consequences are as follows.