## 1 Introduction
In theory, classical machine and deep learning approaches are also applicable in forecasting models for data generation by applying them for long-term \"prediction\" based on the previously predicted data. For example, in [25], the power of a PV generator was forecasted using an artificial neural network (ANN) with measured solar irradiance for the last 3 and 6 days and one forecasted value. The study reported a total of 7% forecasting error. A similar approach was used in [26], where a hybrid ANN model was applied for forecasting the power output of a thin-film PV installation. The study achieved a relative root mean square error between 3.59% and 8.65%, depending on the solar radiation intensity. Even though the authors did not investigate the application of their models for generating synthetic data, they could be combined with a random generator for forecasting solar irradiation. Another major approach to generating synthetic load profiles is the application of probabilistic models, particularly those based on experimentally obtained data. Among these, Markov chains and other ML techniques offer a robust mathematical framework for modeling and predicting energy consumption patterns while preserving key statistical and temporal properties. By leveraging historical data, synthetic load profiles can support simulation-based analysis, demand-side management, and the optimization of renewable energy systems. Markov chains are considered a less powerful apparatus than machine learning models, but they are a lighter and more efficient alternative recommended for usage with time series data [7]. In [27], the authors examined the generation of household electrical load schedules using Markov chains. Their main goal was to create synthetic electricity consumption schedules that reflect the actual electricity consumption patterns in different types of dwellings. A first-order Markov chain based on a 24 \(\times\) 24 transition matrix was used to model the transition between different levels of electricity consumption. The analysis was based on consumption data collected at 30 min intervals over six months from five different types of dwellings in Ireland. The model successfully reproduced the basic statistical characteristics, such as mean and standard deviation. However, the synthetic profiles failed to capture the temporal structure of peaks and troughs in consumption. Another study [28] aimed to find a method for generating synthetic energy production and consumption profiles that reflect the statistical and temporal characteristics of real data, focused on creating multiple scenarios that can be used for microgrid design and optimization. A Markov chain approach was proposed, based on historical data for electricity consumption, heat costs, and solar production. The approach combines clustering to reduce data and determine transition matrices for different periods (in this case, hourly intervals). The synthetic profiles successfully reproduced the main statistical characteristics of the real data, such as averages, seasonality, and time cycles. The approach shows flexibility, allowing both long-term forecasts for design and short-term forecasts for microgrid management. A model for the synthetic generation of solar irradiation data using Markov chains and time segmentation was proposed in [29]. Solar irradiation is classified into four categories: low, medium, high, and very high, according to the intensity of solar radiation. The data are divided into time segments, and a separate transition matrix is calculated for each segment. The algorithm uses these matrices to generate synthetic values of irradiation for each time interval. Such an approach is applicable in the design of energy storage systems and optimization of smart grids; however, a calibration of the model to a specific geographical location is required. An application of Markov models to predict future states based on user behavior and sensor data is described in [30].