Local Whittle estimation of fractional integration and some of its variants

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Estimators of Long-Memory: Fourier versus Wavelets (2008, methodology): “ationarity must be guessed in advance. An alternative deﬁnition of M(d) process has been introduced by Robinson (1994) and later used by some authors (see Tanaka (1999), Shimotsu and Phillips (2005), Shimotsu and Phillips (2006)). The memory parameter dplays a central role in the deﬁnition of M(d) p”
EXACT LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION WITH UNKNOWN MEAN AND TIME TREND (2009, unknown): “Second, the untapered local Whittle estimator has N(0, 14) asymptotic distribution under both Type I (Robinson, 1995b) and Type II (Shimotsu and Phillips, 2006) processes.”
Simple (but effective) tests of long memory versus structural breaks (2006, background): “To show (22), the equation in the last line of page 230 of Shimotsu and Phillips (2006) provide a counterpart of (4.8) of Robinson (1995) for X t generated by (4): E r j=1 (G −1 0 λ 2d 0”
Risk and return: Long-run relations, fractional cointegration, and return predictability $ (2013, methodology): “We rely on the local Whittle approach for estimating d for the error term n t , together with the techniques developed by Christensen and Nielsen (2006) and Shimotsu and Phillips (2006) for estimating the asymptotic standard errors.”