It is known that, in the presence of short memory components, the estimation of the fractional parameter d in an Autoregressive Fractionally Integrated Moving Average, ARFIMA(p, d, q), process leads to some difficulties (Smith et al. (1997)). In this paper, we continue the efforts made by Smith et al. (1997) by conducting a simulation study to evaluate the convergence properties of the iterative estimation procedure suggested by Hosking (1981 ). In this conteJ...'t we consider some semiparametric approaches and a parametric method proposed by Whittle (1953). We also investigate the method proposed by Robinson (1995a) and a modification using the smoothed periodogram function.