## 6 Conclusions  
The main objective is to employ forecasting techniques that can effectively address the uncertainty of the PV power fluctuations. These methods can predict the power output of a PV system over a specific period with a certain level of accuracy, which can help manage the associated uncertainties. In our research, we utilized a combination of forecasting techniques, including machine-learning algorithms and statistical models, to enhance the precision of the predictions. In particular, we investigated the potential advantages of combining AHW with LSTM and BO algorithms within an HM framework for time-series forecasting. AHW is a seasonal decomposition method that can be employed to model and forecast time-series data. LSTM is an RNN that is particularly suitable for processing long-term dependencies in sequential data. BO is an optimization algorithm that utilizes probabilistic models to explore the search space efficiently and identify the optimal solution. The experimental results showed that by combining these three techniques, it may be possible to enhance the accuracy and efficiency of time-series data forecasting. LSTM can be used to capture long-term dependencies in the data, whereas the AHW algorithm can be used to model and forecast seasonal patterns. The proposed model does not require substantial computational resources or specialized expertise for implementation and fine-tuning. In the reference case study, the configuration times were not greater than 24 min of computation on a 6-core processor with 16 GB of RAM (i.e., a typical laptop) to be implemented and fine-tuned. Furthermore, no expertise is required from the analyst because the GA and BO algorithms are used to automatically fine-tune the parameters of AHW and LSTM to achieve superior results. Therefore, this approach is suitable for small operations or regions with a limited computational infrastructure. Through our analysis, we found that integrating statistical modeling with the LSTM and BO algorithms led to more accurate forecasting results compared with using each method alone. These findings imply that the integration of statistical modeling with LSTM and BO algorithms can improve the accuracy and reliability of time-series forecasting of PV energy production. By combining these methods, we can develop more precise and reliable forecasting models that can inform decision making and resource management in this field. Our research has implications for forecasting PV power data when only historical data of PV power generation are available and NWP data are inaccessible. The proposed methodology can be applied to various geographic locations, climates, and types of renewable energy sources, without limitations. To enhance the current approach, future research could investigate its effectiveness for other renewable energy sources such as wind or hydropower by broadening the scope of this study. Additionally, other time-series models, such as the exponential smoothing state-space model or the seasonal decomposition of the time-series model, can be explored when integrated with the LSTM and BO algorithms. Finally, investigating the impact of data quality, such as missing data, noisy data, or data with outliers, on the effectiveness of the proposed methodology can provide valuable insights. Finally, it is important to note that the techniques explored in this study rely heavily on the availability of large historical datasets to capture patterns effectively, learn representations, and make accurate discoveries. Therefore, ensuring access to such datasets is essential for successful application of these techniques. In regions where there is a lack of historical data or when estimating outputs for new installations, it is recommended to utilize physical models that offer deterministic closed-form solutions for the PVPF. However, these models rely on data related to solar irradiance and require detailed parameters for PV plants and expert analyses.