The inverse autocorrelations of a time series are defined to be the autocorrelations associated with the inverse of the spectral density of the series. They can be estimated by calculating the autocorrelations associated with the inverse of a spectral density estimate. Two diierent methods of estimating the inverse autocorrelations arise from two different methods of estimating the spectral density—autoregressive and periodogram smoothing. The estimates of the inverse autocorrelations are used to assist in identifying a parsimonious, moving-average, autoregressive model for the series and to provide rough initial estimates of the parameters for an iterative search for the maximum of the likelihood function. The techniques discussed are applied to chemical process concentration readings, wind velocity measurements, and moon seismic data.