The development of theory of autoregressive fractionally integrated moving average (ARFIMA) process has enabled empirical researchers to observe strong temporal dependence in many financial and economic time series. Time series with a strong temporal dependence are called long-range-dependent or long-memory series which implies that observations of distance past have powerful influence on the recent ones.
The most common method of modelling the long-memory processes is allowing the differencing parameter (d) to assume non-integer values.
A very popular method, mostly due to its computational simplicity, of estimating the differencing parameter of a long-memory process is provided by Geweke and Porter-Hudak (1983). This is a semi-parametric estimation approach for it only estimates the differencing parameter d. A simulation study by Hurvich, et al. (1998) indicates that the choice of periodogram ordinate m from the sample size T, as originally sggested by GPH, is suboptimal and could lead to inferior performance compared to the asymptotically optimal choice of m.
In this paper we use the plug-in method of Hurvuch and Deo (1999) to estimate the differencing parameters for testing the persistence of shocks to a number of daily dollar exchange rates and then compare the results with estimated values of d's of the same series that are based on u=0.5, 0.55, 0.60, as suggested in Geweke and Porter-Hudak (1983).