When random input data are not or cannot be measured, then only the available output data can be fitted to a time domain autoregressive moving-average (ARMA) model. This estimation process always produces a minimum phase system. This means that only the natural frequency and damping ratio of the system can be identified. The mode shape cannot be determined uniquely. A new approach has been introduced in this paper to overcome these problems when a structure is randomly excited. The selection of the sampling interval for estimating the modal parameters from a randomly excited structure subjected to unmeasurable inputs is also considered. The theoretical basis of the procedure is presented together with simulation results.