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An exact form of the local Whittle likelihood is studied with the intent of developing a general purpose estimation procedure for the memory parameter ( d ) that does not rely on tapering or diﬀerencing preﬁlters. The resulting exact local Whittle estimator is shown to be consistent and to have the same N (0,1/4) limit distribution for all values of d if the optimization covers an interval of width less than 9/2 and the initial value of the process is known.
Shimotsu, Katsumi and Phillips, Peter C.B., "Local Whittle Estimation of Fractional Integration" (2002). Cowles Foundation Discussion Papers. 1631.