Log Periodogram Regression: The Nonstationary Case

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Unit root log periodogram regression (2007, background): “Kim and Phillips (1999) showed LP regression is consistent for 1 2 odo1 without requiring Gaussianity or trimming, as well as demonstrating inconsistency for d41.”
Local Whittle estimation in nonstationary and unit root cases (2004, background): “Kim and Phillips (1999) showed that the LP regression estimator also converges to unity whend0 > 1.”
Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration (2005, unknown): “Recently, Kim and Phillips ( 1999 ) and Velasco ( 1999b ) demonstrated that the range of consistency is d ∈ ( − 1/2,1] and the range of asymptotic normality is d ∈ ( − 1/2,3/4).”
EXACT LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION WITH UNKNOWN MEAN AND TIME TREND (2009, unknown): “For instance, they have a nonnormal limit distribution for d ∈ [ (3)4 ,1], and they converge to unity in probability and are inconsistent for d > 1 (Kim and Phillips, 2006; Phillips, 2007; Phillips and Shimotsu, 2004). To avoid inconsistency and an unreliable basis for inference when d may be larger”
LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION FOR NONLINEAR PROCESSES (2007, background): “The asymptotic properties of LP regression have been investigated by Robinson (1995a) and Velasco (1999a, 2000) among others for Type I processes and by Kim and Phillips (1999) and Phillips (1999b) for Type II processes.”