In the realm of industrial engineering and management, production forecasting is a pivotal topic that profoundly influences productivity and the optimization of production processes. By developing a precise prediction model, companies can significantly enhance production planning, control production, minimize stoppages, optimize inventories, and boost machinery productivity. This study delves into the production processes of the SAIPA Automotive Group and proposes an accurate prediction model. Using statistical time series forecast models, including the Box-Jenkins method and the Rolling forecast approach, the study reveals that these models, particularly the Auto Regressive Integrated Moving Average eXogenous (ARIMAX) model, excel at daily production prediction. Conversely, the Auto Regressive Integrated Moving Average (ARIMA) and Autoregressive (AR) models demonstrate superior efficiency in trend-based production prediction. Additionally, the Seasonal Auto Regressive Integrated Moving Average (SARIMA) and Seasonal Auto Regressive Integrated Moving Average eXogenous (SARIMAX) models performed worse. The application of time series tools and the rolling forecast approach has also led to a notable reduction in model errors.