Abstract.Two‐stage estimators have been proposed in fractional autoregressive integrated moving‐average (ARIMA) systems which first estimate the long‐run features of the system semi‐parametrically and then estimate the short‐run features by usual methods in a second stage. Although asymptotic theory is available for the estimates in the first stage of such a procedure, we are aware of no results concerning the estimates in the second stage. In this paper we provide a stochastic order of magnitude associated with an estimator in this class and discuss th