# Predictive Modeling of Photovoltaic Energy Yield Using an ARIMA Approach
## 1 Introduction  
Environmental problems are among today's challenges that humanity must deal with to reduce environmental pollution and the greenhouse effect [1, 2]. Growing energy consumption as a result of population growth and increasing demand from developing countries leads to the search for alternative energy sources [3]. Many scientists consider solar energy as one of the alternative sustainable energy resources that is cheap and inexhaustible [4]. The use of solar energy in the global energy mix has increased considerably, especially after the war in Europe. In the increasing need for sustainable and ecological energy sources, photovoltaic (PV) systems have become a key factor in the transition to renewable energy sources. The photovoltaic industry has experienced rapid growth throughout the world, as well as in Bulgaria [5, 6]. Technology advances, lower production costs, and government policies promoting renewable energy all contribute to the development of photovoltaic systems globally. Photovoltaics are leading in installed capacity in Europe, the USA, and China, but interest in the technology is also growing in developing countries such as Bulgaria. According to a report by the International Energy Agency [7], global investments in clean energy will almost double by 2024. Nowadays, more money is invested in solar PV than in all other electricity generation technologies combined. In 2024, investment in solar PV is expected togrow to USD 500 billion due to falling prices of solar modules [8]. Bulgaria currently has 6757 MW of installed renewable energy capacity, of which 3612 MW (53.4%) is solar power, 2375 MW is hydroelectric power, 707 MW is wind power, and 64 MW comes from other sources [9; 10]. Solar energy as a renewable energy source is becoming increasingly popular and preferred by many households to reduce costs. In Bulgaria, during May, June, July, August, and September, solar energy is high, and many households build photovoltaic systems on the roofs of their houses. Thus, they can use solar energy to reduce their electricity bills [11; 12]. Currently, machine learning-based methods are employed for PV data forecasting. In [13], a machine learning-based weighted average ensemble model is introduced to enhance photovoltaic power forecasting by integrating multiple imputation methods tailored to varying weather conditions. This approach outperforms single-imputation models by adjusting weights based on \"sky status\", yielding improved accuracy in RMSE and MAE metrics under scenarios with missing data. The paper [14] compares four probabilistic forecasting methods for day-ahead photovoltaic power generation, highlighting the superior performance of statistical methods over physical models. Notably, conformalized quantile regression achieved the highest probabilistic accuracy, emphasizing the greater importance of weather forecasts over autoregressive predictors in improving forecast reliability. The work of [15] explores various machine learning algorithms for solar power forecasting in Indian solar parks, demonstrating their effectiveness in predicting power generation compared to the Smart Persistence (SP) method. The results highlight that machine learning models significantly improve forecast accuracy, supporting enhanced system stability and optimized hydropower dispatch. What is more, deep learning is heavily used for forecasting PV-related data. The study [16] introduces a two-stage neural network (NN) optimization method using Optuna and random forest integration to improve solar PV power forecasting accuracy and ease of modeling. Tested on the New-Incheon Sonae dataset, the method achieves superior performance with an MAE of 149.53 kW and an RMSE of 202.00 kW, outperforming attention-based deep learning benchmarks, offering significant potential for application in the Republic of Korea's energy sector.