## 3 Experiment and Results
### Parameter Setting  
Parameter settings and initializations important to the methods applied included the following:  
Input dimension. For the input vector, we set varying values of 1-8 for the input vector based on the ten-minute wind speed data and values of 1-6 for the input vector based on the 10-min wind power and wind speed data. The results of our empirical study indicated that the forecasting accuracy was at its best when the input vector dimension was 6.  
SSA decomposition and EEMD denoising. For the previously mentioned SSA decomposition stage, the window length \(L\) and the principal components were the two most vital factors. On the basis of the trial-and-error method, \(L\) was set to 24 for ten-minute intervals to assess the wind speed transition and wind power from observation Sites 1 to Site 4 due to the homogeneity of the data structure among intervals. Thirteen principal components were selected for all sites. Table 3 shows the eigenvalue contributions to the various low- and high-frequency data groups in the time sequences. Taking the Site 1 wind speed series as an example, the principal components related to the first 13 eigenvalues accounted for 97.7643% of the variability, representing the main trend in the series. Further denoising was carried out for the high-frequency components. By parity of reasoning, the wind power time series data from the four sites were also analyzed by SSA using the trial-and-error and principal component analysis methods. The details are given in Table 3. For the EEMD  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & **Definition** & **Equation** \\ \hline MAE & The mean absolute error of \(N\) & MAE = \(\frac{1}{N}\sum_{i=1}^{N}\left|y_{a}-\hat{y}_{a}\right|\) \\ RMSE & The root mean square error of \(N\) & RMSE = \(\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left(y_{a}-\hat{y}_{a}\right)^{2}}\) \\ MAPE & The mean absolute percentage error of & MAPE = \(\frac{1}{N}\sum_{i=1}^{N}\frac{y_{a}-\hat{y}_{i}}{y_{a}}\) \\ STD of APE & The standard deviation of absolute percentage error of \(N\) forecasting results & STDAPE = \(\sqrt{\text{Var}\left(\frac{y_{a}-\hat{y}_{a}}{y_{a}}\right)}\) \\ R\({}^{2}\) & The goodness-of-forecasting fit & R\({}^{2}\) = \(\frac{\sum_{i=1}^{N}\left(y_{a}-\hat{y}_{i}\right)-\sum_{i=1}^{N}\left(y_{a}- \hat{y}_{a}\right)}{\sum_{i=1}^{N}\left(y_{a}-\hat{y}_{a}\right)}\) \\ DA & Directions or turning points between actual and forecasting values & DA = \(\frac{100}{N-1}\sum_{n=1}^{N-1}m_{t}\) \\ U1 & U-Statistic of 1-order & U1 = \(\frac{\sqrt{\frac{1}{N}\sum_{n=1}^{N-1}\left(y_{a}-\hat{y}_{n}\right)^{2}}}{ \sqrt{\frac{1}{N}\sum_{n=1}^{N}\left(y_{a}\right)^{2}}+\sqrt{\frac{1}{N}\sum_{n =1}^{N}\left(\hat{y}_{a}\right)^{2}}}\) \\ U2 & U2 = \(\frac{\sqrt{\frac{1}{N}\sum_{n=1}^{N}\left(\frac{y_{a}-\hat{y}_{n}}{y_{n}} \right)^{2}}}{\sqrt{\frac{1}{N}\sum_{n=1}^{N}\left(\frac{y_{a}-\hat{y}_{n}}{y_{ n}}\right)^{2}}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The forecasting metric for each model.  
denoising stage, the number of IMFs was acquired by the formula \(\log_{2}\!N-1\), where \(N\) is the length of the series. The IMFs ranged from high-frequency to low-frequency.  
For MODA, the population size of the dragonfly was 40, the archive size was 500, and the maximum number of iterations was 200.  
For each artificial neural network, the building and training of the network were nearly parallel. There were 5 input layer neurons, 20 initial hidden layer neurons, and 1 output layer neuron.