Estimation of the memory parameter ( d ) is considered for models of nonstationary fractionally integrated time series with d > (1/2). It is shown that the log periodogram regression estimator of d is inconsistent when 1 < d < 2 and is consistent when (1/2) < d = 1. For d > 1, the estimator is shown to converge in probability to unity.
Kim, Chang Sik and Phillips, Peter C.B., "Log Periodogram Regression: The Nonstationary Case" (2006). Cowles Foundation Discussion Papers. 1880.