Battery Electric Vehicles (BEVs) have matured and are now widely available for consumers globally. BEVs rely solely on stored electrical energy in their battery packs to power electric motors, without any assistance from combustion engines. This shift in automotive technology has placed new demands on electricity utility providers, who must enhance their electricity generation and distribution infrastructure to support the growing number of BEV charging stations. Due to the limited availability of BEV charging data, this study utilizes data from the My Electric Avenue project, covering the period from 1st January 2014 to 15th December 2014. The data, originally in the form of start-stop charging events, is transformed into counts of simultaneous charging events to analyze charging behavior patterns. Then, the Box-Jenkins method is applied to model and forecast the BEV data charging pattern during the early stages of BEV adoption. The Box-Jenkins model, particularly the Seasonal ARIMA (SARIMA) variant, is selected for its practicality and robust performance in time series forecasting. The Box-Jenkins models is assessed using model selection criteria such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), as well as forecast evaluation metrics including Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). The best-performing time series model is identified as SARIMA \((0,1,1) (0,1,1)_7\) , which achieves the lowest AIC value of 265.973 and a MAPE of 12.863%. The results demonstrate that the SARIMA model, is well-suited for BEV charging time series data and is effective in forecasting future electricity demand in regions at the early stage of BEV adoption. This can provide utility companies with a reliable tool to anticipate and manage the increased load on their grids as BEV usage expands.