# Efficient Machine Learning-Based Prediction of Solar Irradiance Using Multi-Site Data
## 3 Results and Discussion
### Hourly GHI Prediction and Link with Time-Lagged Versions  
In the third step, we examined how model performance varied across all stations when using different time-shifting windows. The analysis was mainly extended to 1-h shifting and forecasting. Table 8 comprehensively compares all metrics for the 30 min- and 1 h-lagged temporal shifts. It is observed that extending the forecasting and shifting horizons results in a deterioration in the model's performance at the NELHA station, particularly evident in the RMSE metrics. The best-performing model also changed to the MLP. Similar observations were made for the NWTC station, where the ExtraTrees model proved to be the best performer. However, for other stations, the models performed well for both forecasting horizons. This indicates that the models effectively account for the impact of the shift and the forecasting horizon due to the efficient feature selection technique, which includes the shifted versions of the GHI. One possible reason for performance degradation over varying time shifts, especially with increased data versions, is the reduction in the number of samples in the dataset, particularly when starting with a lower sampling rate. This limitation means that models have less data to analyze. It is also noteworthy that for the 30-min shift, the MLP was the best-performing model at two different stations. For the 1-h shift, it was selected as the best performer at three stations. This pattern aligns with the fact that neural networks, including MLPs, are powerful deep learning models, particularly effective for mid-to-long-term forecasting horizons, making this level of performance expected. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{**NELHA Station**} & & & & & \\ \hline
**Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** & **MAPE** & **Median AE** & \(\mathbf{D^{2}}\) & **Composition** \\ \hline
**Stacking** & 0.96 & 63.61 & 28.25 & 5.69 \(\times 10^{11}\) & 2.58 & 0.88 & GradientBoosting, MLP \\ \hline \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & & & \\ \hline
**Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** & **MAPE** & **Median AE** & \(\mathbf{D^{2}}\) & **Composition** \\ \hline
**Stacking** & 0.95 & 61.87 & 25.96 & 3.83 \(\times 10^{10}\) & 1.88 & 0.87 & MLP, CatBoost, GradientBoosting \\ \hline \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & & & \\ \hline
**HSU Station** & & & & & & & \\ \hline
**Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** & **MAPE** & **Median AE** & \(\mathbf{D^{2}}\) & **Composition** \\ \hline
**Stacking** & 0.97 & 45.59 & 18.46 & 0.64 & 1.18 & 0.89 & CatBoost, RandomForest \\ \hline \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & & & \\ \hline
**Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** & **MAPE** & **Median AE** & \(\mathbf{D^{2}}\) & **Composition** \\ \hline
**Stacking** & 0.97 & 60.88 & 26.90 & 4.88 \(\times 10^{11}\) & 2.4 & 0.89 & GradientBoosting, MLP \\ \hline \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & & \\ \hline
**NWTC Station** & & & & & & & \\ \hline
**Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** & **MAPE** & **Median AE** & \(\mathbf{D^{2}}\) & **Composition** \\ \hline
**Stacking** & 0.994 & 69.888 & 28.827 & 0.523 & 2.942 & 0.904 & GradientBoosting, RandomForest \\ \hline \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & & \\ \hline
**Rad2 ON Station** & & & & & & & \\ \hline
**Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** & **MAPE** & **Median AE** & \(\mathbf{D^{2}}\) & **Composition** \\ \hline
**Stacking** & 0.90 & 98.940 & 28.602 & 1.04174 \(\times\) 10\({}^{15}\) & 1.401 & 0.853 & GradientBoosting, ExtraTrees \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results for different stations using a 30-min shift.