# Efficient Machine Learning-Based Prediction of Solar Irradiance Using Multi-Site Data
## 3 Results and Discussion
### Benchmarking with ARIMA and Individual Non-Shifted Features  
A comprehensive benchmarking strategy was employed to evaluate the effectiveness of our proposed forecasting solution in comparison with established techniques. As a first step, the results were assessed against those produced by the Seasonal AutoRegressive Integrated Moving Average with Exogenous Regressors (SARIMAX) model. SARIMAX is a well-known statistical time-series model that captures both non-seasonal and seasonal patterns, while also allowing for the inclusion of external covariates. It serves as a strong baseline due to its interpretability and proven performance in univariate forecasting tasks. Subsequently, a second level of benchmarking was conducted using classical machine learning models trained on engineered features, particularly those exhibiting a strong correlation with the target variable, GHI. To ensure a fair and consistent comparison, the same input window size (24 h of historical data) was maintained across all models. This alignment enabled the models to benefit equally from temporal context, avoiding any bias introduced by differing input configurations. The performance of each model was evaluated using standard metrics such as the coefficient of determination \(R^{2}\) and the RMSE, providing a robust and interpretable comparison framework.  
It is first evident that the standalone machine learning models incorporating shifted input features (as shown in Figure 17a) exhibit significantly greater robustness and predictive capability than the SARIMAX model. SARIMAX fails to effectively capture the temporal dependencies and complex non-linear dynamics inherent in the meteorological station data. This limitation is quantitatively reflected in its higher RMSE values relative to all the tested standalone models. One contributing factor to this underperformance is SARIMAX's reliance on substantial historical data to accurately estimate its autoregressive and seasonal parameters, a condition not fully satisfied within the current training regime. In addition to its limited forecasting precision, SARIMAX suffers from considerable computational inefficiency. Training the model on only 20,000 samples required approximately 307.5 s, while the same dataset was processed by the RandomForest in 66.8 s, by XGBoost in 1.08 s, and by CatBoost in 12.0 s. These results clearly raise concerns about SARIMAX's scalability and suitability for real-time deployment. In a second experiment, we evaluated the impact of using only features with a strong correlation to the target variable. For benchmarking purposes, the UNLV station was selected, as illustrated in Figure 17b. This setup retained a fixed time shift of 30 min. The performance of all models exhibited slight, yet observable degradation. For instance, the MLP model experienced a pronounced increase in RMSE, rising by over 7 units compared to its previous value with temporal shifts (42.82). Additionally, the \(R^{2}\) score fell below the 0.90 threshold, reflecting a degradation of approximately 0.08 relative to its earlier performance (0.98). These results emphasize the critical importance of careful feature selection, particularly in time-series contexts, where lag-based or shift-based variables can significantly enhance model expressiveness. Furthermore, the findings underline important practical considerations regarding the deployment of forecasting models. While classical models like SARIMAX offer strong statistical foundations, their high training time and dependency on extensive data make them less ideal for embedded or resource-constrained environments. In contrast, modern machine learning models, especially tree-based ensembles and neural networks, offer a more favorable balance between accuracy, speed, and scalability for real-time or edge computing scenarios.