## 4 Results and Discussion
### Development of Univariate Hybrid Model  
The hybrid model based on a univariate wind forecasting model using persistence, classical time series, and machine learning models was developed after analyzing the performance of the model for predicting each time step of the total forecast horizon. For this, wind data of four case study sites were analyzed. After analyzing the performance of the individual model, a liner optimization was performed to minimize the performance metrics values to obtain thevweight function for each model contributing to the hybrid wind speed prediction model. The test data were divided again into the test and train data to evaluate the performance of the individual model and thus determine the weight function on the forecasted value on the test data. Then, the weight function was applied to the wind speed prediction value on the training dataset, thus determining the wind speed prediction value from the hybrid model. The performance results of the individual model of each time step of the forecast horizon are presented in Tables 6-9. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**RMSE**} \\ \hline
**Models** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **Average** \\ \hline PM & 0.68 & 0.98 & 1.28 & 0.47 & 0.14 & 2.88 & 1.07 \\ WEBSEC & 0.05 & 2.28 & 0.53 & 0.97 & 1.2 & 0.97 & 1.00 \\ ARIMA & 0.13 & 0.44 & 0.81 & 1.12 & 1.33 & 1.45 & 0.88 \\ SVR & 2.49 & 2.97 & 2.97 & 3.29 & 2.03 & 1.49 & 2.54 \\ LSTM & 0.05 & 2.28 & 0.53 & 0.97 & 1.2 & 0.97 & 1.00 \\ \hline \hline \multicolumn{6}{c}{**MAE**} \\ \hline
**Models** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **Average** \\ \hline PM & 0.68 & 0.98 & 1.28 & 0.474 & 0.146 & 2.88 & 1.07 \\ WEBSEC & 0.39 & 2.3 & 0.78 & 1.52 & 2.37 & 2.83 & 1.70 \\ ARIMA & 0.2 & 0.488 & 0.56 & 1.67 & 2.51 & 0.4 & 0.97 \\ SVR & 0.2 & 0.38 & 0.008 & 1.21 & 0.57 & 2.99 & 0.89 \\ LSTM & 0.39 & 2.35 & 0.78 & 1.52 & 2.37 & 2.83 & 1.71 \\ \hline \hline \multicolumn{6}{c}{**MAPE**} \\ \hline
**Models** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **Average** \\ \hline PM & 6.75 & 9.94 & 13.38 & 4.56 & 1.32 & 36.17 & 12.02 \\ WEBSEC & 3.92 & 23.52 & 0.08 & 0.14 & 0.21 & 0.35 & 4.70 \\ ARIMA & 2.004 & 4.93 & 5.89 & 16.16 & 22.81 & 5.05 & 9.47 \\ SVR & 1.9 & 3.8 & 0.9 & 11.7 & 5.2 & 37.57 & 10.18 \\ LSTM & 3.9 & 23.52 & 8.22 & 14.7 & 21.56 & 0.35 & 12.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance results of different univariate WSP models for South Plains TX region. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**RMSE**} \\ \hline
**Models** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **Average** \\ \hline PM & 2.65 & 2.65 & 2.65 & 2.65 & 2.65 & 2.65 & 2.65 \\ WEBSEC & 0.13 & 0.45 & 2.81 & 3.75 & 1.05 & 0.58 & 1.46 \\ ARIMA & 3.27 & 3.17 & 2.97 & 2.75 & 2.6 & 2.48 & 2.87 \\ SVR & 4.08 & 2.85 & 1.44 & 0.56 & 0.07 & 0.38 & 1.56 \\ LSTM & 0.03 & 0.04 & 0.06 & 0.07 & 0.09 & 0.1 & 0.07 \\ \hline \hline \multicolumn{6}{c}{**MAE**} \\ \hline
**Models** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **Average** \\ \hline PM & 0.29 & 1.63 & 2.59 & 3.27 & 3.813 & 4.3 & 2.65 \\ WEBSEC & 2.21 & 1.47 & 2.75 & 4.37 & 2.21 & 1.06 & 2.35 \\ ARIMA & 0.92 & 2.15 & 2.91 & 3.37 & 3.76 & 4.13 & 2.87 \\ SVR & 0.94 & 1.04 & 0.59 & 0.39 & 0.44 & 0.47 & 0.65 \\ LSTM & 2.3 & 0.96 & 0.01 & 0.69 & 1.2 & 1.75 & 1.15 \\ \hline \hline \multicolumn{6}{c}{**MAPE**} \\ \hline
**Models** & **t = 1** & **t = 2** & **t = 3** & **t = 4** & **t = 5** & **t = 6** & **Average** \\ \hline PM & 3.14 & 20.12 & 36.23 & 50.55 & 64.35 & 79.1 & 42.25 \\ WEBSEC & 23.45 & 18.13 & 38.54 & 67.64 & 37.43 & 19.64 & 34.14 \\ ARIMA & 9.7 & 26.5 & 40.7 & 52.16 & 63.59 & 76.03 & 44.78 \\ SVR & 10.05 & 12.83 & 8.31 & 6.1 & 7.5 & 8.7 & 8.92 \\ LSTM & 24.5 & 11.9 & 0.014 & 10.8 & 21.2 & 32.2 & 16.77 \\ \hline \hline \end{tabular}
\end{table}