  This work proposes a new minimum distance estimator (MDE) for the parameters
of short and long memory models. This bias corrected minimum distance estimator
(BCMDE) considers a correction in the usual MDE to account for the bias of the
sample autocorrelation function when the mean is unknown. We prove the weak
consistency of the BCMDE for the general fractional autoregressive moving
average (ARFIMA(p, d, q)) model and derive its asymptotic distribution for some
particular cases. Simulation studies show that the BCMDE presents a good
performance compared to other procedures frequently used in the literature,
such as the maximum likelihood estimator, the Whittle estimator and the MDE.
The results also show that the BCMDE presents, in general, the smallest mean
squared error and is less biased than the MDE when the mean is a non-trivial
function of time.
