## 6 Experiments
### Experiment II: Models Tested with Wind-Speed Data From Site 1  
In order to evaluate the accuracy and stability of the forecasting system, we selected the average results of 100 trials, which were divided into two parts: accuracy and stability. In the accuracy section, we compare the AE, MAE, MSE, and MAPE values for a single model and combined model (as shown in Table 4). \begin{table}
\begin{tabular}{l l c c c c c c c} \hline \hline  & & **Mon** & **Tue** & **Wed** & **Thu** & **Fri** & **Sat** & **Sun** \\ \hline \multirow{4}{*}{AE} & CSPNN & \(-0.0466\) & \(-0.0547\) & \(-0.0269\) & \(-0.0265\) & \(-0.0194\) & \(-0.0261\) & \(-0.0386\) \\  & DE-OSELM & \(-0.0120\) & \(-0.0164\) & \(-0.0108\) & \(-0.0238\) & \(-0.0444\) & \(-0.0108\) & \(-0.0297\) \\  & ARIMA & \(-0.2151\) & \(-0.2508\) & \(-0.2658\) & \(-0.2054\) & \(-0.3563\) & \(-0.3744\) & \(-0.3101\) \\  & HW & \(0.0184\) & \(0.0178\) & \(-0.0187\) & \(0.0043\) & \(-0.0083\) & \(-0.2792\) & \(-0.0068\) \\  & Combined Model & \(-0.0013\) & \(-0.0091\) & \(-0.0158\) & \(-0.0156\) & \(-0.0104\) & \(-0.0119\) & \(0.0047\) \\ \cline{2-10}  & CSBPNN & \(0.2810\) & \(0.2520\) & \(0.2129\) & \(0.2289\) & \(0.4479\) & \(0.4294\) & \(0.3179\) \\  & DE-OSELM & \(0.2759\) & \(0.2531\) & \(0.2144\) & \(0.2234\) & \(0.4472\) & \(0.4282\) & \(0.3182\) \\  & ARIMA & \(0.2770\) & \(0.2638\) & \(0.2717\) & \(0.2363\) & \(0.4559\) & \(0.4312\) & \(0.3255\) \\  & HW & \(0.2942\) & \(0.2652\) & \(0.2366\) & \(0.2324\) & \(0.4252\) & \(0.4153\) & \(0.3412\) \\  & Combined Model & \(0.2420\) & \(0.2520\) & \(0.2141\) & \(0.2207\) & \(0.4445\) & \(0.4196\) & \(0.3161\) \\ \cline{2-10}  & CSBPNN & \(0.1916\) & \(0.1074\) & \(0.0769\) & \(0.0780\) & \(0.4441\) & \(0.3709\) & \(0.1713\) \\  & DE-OSELM & \(0.1876\) & \(0.1075\) & \(0.0754\) & \(0.0812\) & \(0.4351\) & \(0.3705\) & \(0.1695\) \\  & ARIMA & \(0.1818\) & \(0.1591\) & \(0.0873\) & \(0.0821\) & \(0.3966\) & \(0.3914\) & \(0.1287\) \\  & HW & \(0.1999\) & \(0.1107\) & \(0.0926\) & \(0.0882\) & \(0.3486\) & \(0.2850\) & \(0.1901\) \\  & Combined Model & \(0.1812\) & \(0.1053\) & \(0.0752\) & \(0.0771\) & \(0.3322\) & \(0.3580\) & \(0.1269\) \\ \cline{2-10}  & CSBPNN & \(5.908\) & \(3.726\) & \(4.081\) & \(5.173\) & \(5.729\) & \(6.628\) & \(5.103\) \\  & DE-OSELM & \(5.768\) & \(3.728\) & \(4.097\) & \(5.445\) & \(5.748\) & \(5.647\) & \(5.093\) \\ MAPE & ARIMA & \(6.227\) & \(4.299\) & \(5.513\) & \(5.610\) & \(5.967\) & \(6.469\) & \(5.522\) \\  & HW & \(6.493\) & \(3.999\) & \(\omega.4517\) & \(5.509\) & \(5.721\) & \(6.457\) & \(5.446\) \\  & Combined Model & \(5.691\) & \(3.698\) & \(4.078\) & \(5.166\) & \(5.692\) & \(6.443\) & \(5.082\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The forecasting results from Site 1. \begin{table}
\begin{tabular}{l l c c c c c} \hline \hline  & & **Number of** & **Error** & & & & **F-Statistic vs.** \\  & & **Observations** & **Degrees of** & **R-Squared** & **R-Squared** & **Constant** & \(p\)**-Value** \\  & Site 1 & 2008 & 1996 & 0.954 & 0.954 & 4680 & 0 \\ \(y\sim f_{1}(x)\) & Site 2 & 2008 & 1996 & 0.939 & 0.939 & 4300 & 0 \\  & Site 3 & 2008 & 1996 & 0.938 & 0.938 & 4460 & 0 \\ \hline \multirow{4}{*}{\(y\sim f_{2}(x)\)} & Site 1 & 2008 & 1996 & 0.935 & 0.935 & 9840 & 0 \\  & Site 2 & 2008 & 1996 & 0.933 & 0.932 & 9620 & 0 \\  & Site 3 & 2008 & 1996 & 0.936 & 0.936 & 10710 & 0 \\ \hline \multirow{4}{*}{\(y\sim f_{3}(x)\)} & Site 1 & 2008 & 1996 & 0.923 & 0.923 & 8510 & 0 \\  & Site 2 & 2008 & 1996 & 0.925 & 0.924 & 8350 & 0 \\ \cline{1-1}  & Site 3 & 2008 & 1996 & 0.911 & 0.910 & 8460 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Testing wind speed data by adjusting to linear functions or nonlinear functions.