Heating, ventilation, and air conditioning (HVAC) systems account for 30% of the total energy consumption in buildings. Design and implementation of energy-efficient schemes can play a pivotal role in minimizing energy usage. As an important first step towards improved HVAC system controls, this study proposes a new framework for modeling the thermal response of buildings by leveraging data measurements and formulating a data-driven system identification model. The proposed method combines principal component analysis (PCA) to identify the most significant predictors that influence the cooling demand of a building with an auto-regressive integrated moving average with exogenous variables (ARIMAX) model. The performance of the developed model was evaluated both analytically and visually. It was found that our PCA-based ARIMAX (2-0-5) model was able to accurately forecast the cooling demand for the prediction horizon of 7 days. In this work, the actual measurements from a university campus building are used for model development and validation.