## 2 Knowledge and Tools of Model Preparation
Hence, this paper uses five common evaluation standards to assess the point forecasting performance of the proposed model and other comparative models. The five indexes include mean absolute percentage error (MAPE), root mean square error (RMSE), mean absolute error (MAE), direction change (DC) and the index of agreement of forecasting results (IA). Among these indexes, the smaller the values of MAPE, RMSE and MAE, the larger the values of DC and IA, the better the prediction performance. See Table 3 for details of the four indicators. #### 4.2.2 Interval Forecasting Evaluation

For interval prediction, we select four evaluation indexes, which are forecasting interval coverage probability (FICP), forecasting interval normalized average width (FINAW), mean width of the constructed PIs (MPI) and Accumulated width deviation (AWD). Table 4 shows the specific definitions of four indices. Specifically, FICP is the forecasting interval coverage probability of the test data set, which is the main evaluation index of interval prediction. It indicates the coverage effect of the obtained confidence interval to the actual value. Given the confidence level, if FICP is at least greater than or equal to \begin{table}
\begin{tabular}{c c c} \hline \hline
**Indicator** & **Definition** & **Equation** \\ \hline
**FICP** & Forecasting interval coverage probability & \(\textbf{FICP}=\frac{1}{N}\sum\limits_{i=1}^{N}c_{i}\times 100\%\) \\
**FINAW** & Forecasting interval normalized average width & \(\textbf{FINAW}=\frac{1}{N}\sum\limits_{i=1}^{N}\frac{U_{i}-L_{i}}{y_{max}-y_{max} }\times 100\%\) \\
**MPI** & Mean width of the constructed PIs & \(\textbf{MPI}=\sum\limits_{i=1}^{N}\|U_{i}-L_{i}\|\) \\
**AWD** & Accumulated width deviation & \(\textbf{AWD}=\frac{1}{N}\sum\limits_{i=1}^{N}\textbf{AWD}_{i}\) \\ \hline \hline \end{tabular}

* Among the formula, \(U_{i}\) and \(L_{i}\) represent the upper limit and lower limit of forecasting interval, respectively. \(c_{i}\) is the number of the truth value contained in constructed interval. \(N\) represents the testing set number. \(y_{max}\) and \(y_{min}\) are the maximum and minimum of the targets in the whole prediction process. In addition, the calculation expression of \(\textbf{AWD}_{i}\) is \(\textbf{AWD}=\frac{1}{N}\sum\limits_{i=1}^{N}\textbf{AWD}_{i}\), and \(\textbf{AWD}_{i}\) is the width deviation of construction interval of each sample.

\end{table} 
Table 4: Interval prediction evaluation metrics. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Indicator** & **Definition** & **Equation** \\ \hline
**MAPE** & Mean Absolute Percentage Error & \(\textbf{MAPE}=\frac{1}{N}\sum\limits_{i=1}^{N}\left|\frac{y_{i}-\hat{y}_{i}}{y_ {i}}\right|\cdot 100\%\) \\
**MAE** & Mean Absolute Error & \(\textbf{MAE}=\frac{1}{N}\sum\limits_{i=1}^{N}\left|y_{i}-\hat{y}_{i}\right|\) \\
**RMSE** & Root Mean Square Error & \(\textbf{RMSE}=\sqrt{\frac{1}{N}\cdot\frac{N}{i}\left(y_{i}-\hat{y}_{i}\right)^{2}}\) \\
**DC** & Directional Change & \(\textbf{DC}=\frac{100}{N}\sum\limits_{i=1}^{N-1}a_{i}\) \\
**IA** & Index of agreement & \(\textbf{IA}=1-\) \\  & & \(\sum\limits_{i=1}^{N}\left(y_{i}-\hat{y}_{i}\right)^{2}/\sum\limits_{i=1}^{N} \left(\left|\hat{y}_{i}-\hat{y}_{i}\right|-\left|y_{i}-\hat{y}_{i}\right)^{2}\) \\ \hline \hline \end{tabular}

* Among the formula, \(y_{i}\) and \(\hat{y}_{i}\) is the true and predicted value. \(N\) represents the testing set number. In addition, \(a_{i}\) is the directional factor, and is calculated as \(a_{i}=\begin{cases}0,&\text{\emph{otherwise}}\\ 1,&\text{\emph{if}}((y(t+1)-y(t))(\hat{y}(t+1)-y(t)))>0\end{cases}\).

\end{table} 
Table 3: Point forecasting evaluation metrics. 1-alpha, the constructed interval is valid; otherwise, the constructed interval is invalid. FINAW is the normalized average width of the forecasting interval of the testing set. The cost of reducing the width is diminishing the possibility of expected target covering; increasing the coverage requires increasing the width of the interval, so FICP and FINAW are essentially contradictory.