A clinically important task in diabetes management is the prevention of hypo/hyperglycemic events. In this proof-of-concept paper, we assess the feasibility of approaching the problem with continuous glucose monitoring (CGM) devices. In particular, we study the possibility to predict ahead in time glucose levels by exploiting their recent history monitored every 3 min by a minimally invasive CGM system, the Glucoday, in 28 type 1 diabetic volunteers for 48 h. Simple prediction strategies, based on the description of past glucose data by either a first-order polynomial or a first-order autoregressive (AR) model, both with time-varying parameters determined by weighted least squares, are considered. Results demonstrate that, even by using these simple methods, glucose can be predicted ahead in time, e.g., with a prediction horizon of 30 min crossing of the hypoglycemic threshold can be predicted 20-25 min ahead in time, a sufficient margin to mitigate the event by sugar ingestion.