Dynamics of a large moored floating body in ocean waves involves frequency dependent added mass and radiation damping as well as the linear and nonlinear mooring line characteristics. Usually, the added mass and radiation damping matrices can be estimated either by potential theory-based calculations or by experiments. The nonlinear mooring line properties (usually cubic nonlinearity characterised by a constant) are usually quantified by experimental methods. In this paper, we attempt to use a nonlinear system identification approach, specifically the Reverse Multiple Inputs-Single Output (R-MISO) method, to a single degree of freedom system with linear and cubic nonlinear stiffnesses. The system mass is split into a frequency independent and a frequency dependent component and its damping is frequency dependent. This can serve as a model of a moored floating system with a dominant motion associated with the nonlinear stiffness. The wave diffraction force, the excitation to the system, is assumed known. This can either be calculated or obtained from experiments. For numerical illustration, the case of floating semi- ellipsoid is adopted with dominant sway motion. The motion as well as the loading are simulated assuming PM spectrum and these results have been analysed by the R-MISO method, yielding the frequency dependent added mass and radiation damping, linear as well as the nonlinear stiffness coefficients quite satisfactorily.