Fractional differencing and the ARFIMA model were introduced in the early 1980s by Clive Granger, Roselyne Joyeux, and Jonathan Hosking.
The advantage of fGn over ARFIMA(0,d,0) is that many asymptotic relations hold for finite samples.
[4] An ARFIMA model shares the same form of representation as the ARIMA(p, d, q) process, specifically: In contrast to the ordinary ARIMA process, the "difference parameter", d, is allowed to take non-integer values.
[5] Note that any filtering that would substitute for fractional differencing and integration in this AR(FI)MA model should be similarly invertible as differencing and integration (summing) to avoid information loss.
Such frequency response studies may suggest other similar families of (reversible) filters that might be useful replacements for the "FI" part of the ARFIMA modeling flow, such as the well-known, easy to implement, and minimal distortion high-pass Butterworth filter or similar.