Glucose-insulin interactions in the Type I diabetic patient are approximated in an input-output sense using a third-order Volterra series model. Due to the large number of unique coefficients present in a third-order model, efficient parameter identification methods are developed. Several pruned model structures were examined, and maximum dynamic accuracy was obtained when a linear plus nonlinear diagonal model was employed. Increased steady state accuracy could be obtained by including semi-diagonal and off-diagonal coefficients; however, this increase in static accuracy came at a cost of decreased dynamic accuracy. Furthermore, calculation of semi-diagonal and off-diagonal coefficients requires data acquisition times infeasible for clinical applications. Hence, the linear plus nonlinear diagonal Volterra series model is a well-suited structure for approximating Type I diabetic patient glucose-insulin dynamics using input-output methods.