Thanks to various European directives, individuals are empowered to share and trade electricity within Renewable Energy Communities, enhancing the operational efficiency of local energy systems. The digital transformation of the energy market enables the integration of decentralized energy resources using cloud computing, the Internet of Things, and artificial intelligence. In order to assess the feasibility of new business models based on data-driven solutions, various electricity consumption time series are necessary at this level of aggregation. Since these are currently not yet available in sufficient quality and quantity, and due to data privacy reasons, synthetic time series are essential in the strategic planning of smart grid energy systems. By enabling the simulation of diverse scenarios, they facilitate the integration of new technologies and the development of effective demand response strategies. Moreover, they provide valuable data for assessing novel load forecasting methodologies that are essential to manage energy efficiently and to ensure grid stability. Therefore, this research proposes a methodology to synthesize electricity consumption time series by applying the Box–Jenkins method, an intelligent sampling technique for data augmentation and a probabilistic forecast model. This novel approach emulates the stochastic nature of electricity consumption time series and synthesizes realistic ones of Renewable Energy Communities concerning seasonal as well as short-term variations and stochasticity. Comparing autocorrelations, distributions of values, and principle components of daily sequences between real and synthetic time series, the results exhibit nearly identical characteristics to the original data and, thus, are usable in designing and studying efficient smart grid systems.