(1951) Hurst, H.E. "Long-term storage capacity of reservoirs", Trans. Am. Soc. Civil Engineers, 116, 770-799.
Peters, E.E. (1991), Chaos and Order in the Capital Markets: A New View of Cycles, Prices, and Market Volatility, New York, John Wiley and Sons, 1991.
There is only one maximum when the fractional root d is fixed:
Parameter Scoring OPTMUM
phi1 0.91971795 0.91971515
theta1 0.46713308 0.46712854
d 0 0
sigma 2.0190068 2.0190213
So, d can be estimated before computing the MLE of the ARFIMA process.
For example, we can use the GPH (Geweke Porter-Hudak) estimate to fix d.