Generalised least squares (GLS) estimation of the difference parameter in long memory (ARFIMA) processes

In the problem of estimating the fractional difference parameter in a long-memory time series (ARFIMA) process, the GPH technique is quite popular because of its simplicity and lack of need for prior knowledge of the parameters defining the ARMA processes. However it has now been established that the (OLS) assumptions behind the GPH technique do not hold for these processes in general (e.g. Hurvich and Beltrao, 1993). In view of this, an obvious alternative would be to use the generalised least squares method (GLS) for estimation and inference on this parameter. In this paper, we use the results in Hurvich and Beltrao to propose a GLS procedure for estimating the differencing parameter.