This article presents new expressions related to the discrete version of Ahn, Dittmar, Gallant's quadratic model in discrete time. The new expressions one proposes avoid any recursive equations as in Realdon (2006). This may help and speed up both computation and calibration. Furthermore, a multi factors Quadratic Term Structure Model (QTSM) and a multi factors Affine Term Structure Model (ATSM) are estimated and their relative performance are tested. Finally, the behavior of the QTSM is investigated to understand in which way it is relevant to modelize the Term Structure of Interest Rate.