A stochastic realization method is presented for linear, time-invariant, nonminimum phase systems when only output data are available. The input sequence need not be independent and identically distributed. It must be non-Gaussian, with some special properties that are described. The method proceeds in two stages: first, a minimum phase system is obtained using second-order statistics of the output; then, an all-pass filter is realized by exploiting higher-order statistics of the innovations. The cascade of the minimum-phase and all-pass systems yields the desired nonminimum phase system.