# Efficient Machine Learning-Based Prediction of Solar Irradiance Using Multi-Site Data
## 2 Proposed Solution
### Exploratory Data Analysis
For some stations, the zenith angle can have a positive correlation with the target, while for others, it may have a negative impact. This can also be extended to the azimuth angle. Furthermore, features with a correlation of less than 0.3 can be dropped, which is a threshold used particularly for stations that have strong correlations, exceeding 50%, with the target GHI. Figure 4: _Cont._  
* How is GHI linked to the time-lagged versions? In this step, we focused on the lagged version of the GHI across the three stations ULL, NELHA, and HSU. We performed autocorrelation and partial autocorrelation analyses using the ACF and PACF functions over a 30-min horizon. This involved resampling the data to 30 min intervals and examining how the GHI values are related to past values at intervals of 30 min, 1 h, and 1.5 h. We considered the NELHA station as an example for the tests. The results of these analyses are shown in Figure 5. For the NELHA station, the time-lagged versions exhibit degrading behavior over time. The PACF, on the other hand, indicates that the current GHI value is primarily linked to two highly correlated past values. Additionally, smaller correlation values extend up to five past values, which correspond to a time lag of up to 3 h. A similar observation is noted for the ULL and HSU stations, where these lagged versions of GHI are mainly correlated with the values from the last 30 min. This raises another question about how many historical shifts can influence the final results. As detailed in the previous analysis, a notable relationship exists between the shifted and current values of GHI. This relationship is particularly significant when constructing data windows for prediction models. Three main machine learning models--RandomForest (RF), CatBoost, and Multi-Layer Perceptron (MLP)--were employed to analyze the impact of these shifted values on GHI prediction. The selection of these models was based on their demonstrated efficacy in previous research on GHI prediction [4]. A thorough analysis was conducted for at least eight past shifts, with the results illustrated in Figures 6 and 7 for 30 min-ahead, 1 h-ahead, and 2 h-ahead forecasting. The analysis of the shift influence on the variations in \(R^{2}\) and RMSE was performed for all the stations across 8 shifts. For \(R^{2}\), it can be observed that for a 30 min shift, all stations exhibit a consistent result across the 8 shifts, except NWTC and, to some extent, the ULL station. However, when using shifts with higher time intervals, such as 1 h and 2 h, the results become unstable, except for the UNLV station, which shows stable performance. This could indicate that, regardless of the shift considered, the UNLV station's model performance will remain stable. For RMSE, stable performance is observed for a 30 min shift, except for the NWTC station. For 1 h and 2 h shifts, across the 8 shifted values, a non-stable performance is observed for all stations, with  
Figure 4: Correlation analysis for the different stations with GHI: (**a**) NELHA, (**b**) ULL, (**c**) HSU, (**d**) UNLV, (**e**) RAZON, and (**f**) NWTC. minimal instability for the UNLV station. It can be concluded that the shift changes impact the \(R^{2}\) and RMSE performance values for all stations, except for the UNLV station, where the change is minimal yet exists. Figure 5: ACF and PACF for **(a)** NELHA, **(b)** ULL, **(c)** HSU, **(d)** UNLV, **(e)** RAZON, and **(f)** NWTC. * Which features hold significant impact as predictors? In alignment with the previous procedure, a tree average importance technique was applied to the three stations NELHA, HSU, and ULL to identify the optimal features that lead to the best outcomes within the regressors. For the NELHA site, when considering only the 10 most important features, it was found that the lagged version of GHI up to 30 min (from GHI at T-1 to GHI at T-30 min), the accumulated global irradiance up to a 30 min lag, and up to three lags were the most impactful features for predicting GHI at T+30 min.