Active control of high-speed and high Reynolds number axisymmetric jets for noise attenuation and bulk mixing enhancement is a topic of great current interest. An essential initial step in the implementation of feedback control to achieve the above goals is the development of a reduced-order model of the unforced jet. A number of modeling strategies are formulated hereby, and they are evaluated using an existing direct numerical simulation database of an unforced jet similar to our experimental configuration. A combination of proper orthogonal decomposition, spectral stochastic estimation, and Galerkin projection is used to derive the model from empirical data. Simulations of the reduced-order model are demonstrated to be sufficiently faithful to the full-order original simulation results to warrant its use for future control design.