This paper tests the hypothesis that a "universal," data-driven model can be developed based on glucose data from one diabetic subject, and subsequently applied to predict subcutaneous glucose concentrations of other subjects, even of those with different types of diabetes. We employed three separate studies, each utilizing a different continuous glucose monitoring (CGM) device, to verify the model's universality. Two out of the three studies involved subjects with type 1 diabetes and the other one with type 2 diabetes. We first filtered the subcutaneous glucose concentration data by imposing constraints on their rate of change. Then, using the filtered data, we developed data-driven autoregressive models of order 30, and used them to make short-term, 30-min-ahead glucose-concentration predictions. We used same-subject model predictions as a reference for comparisons against cross-subject and cross-study model predictions, which were evaluated using the root-mean-squared error (RMSE) and Clarke error grid analysis (EGA). We found that, for each studied subject, the average cross-subject and cross-study RMSEs of the predictions were small and indistinguishable from those obtained with the same-subject models. These observations were corroborated by EGA, where better than 99.0% of the paired sensor-predicted glucose concentrations lay in the clinically acceptable zone A. In addition, the predictive capability of the models was found not to be affected by diabetes type, subject age, CGM device, and interindividual differences. We conclude that it is feasible to develop universal glucose models that allow for clinical use of predictive algorithms and CGM devices for proactive therapy of diabetic patients.