Local Whittle estimation in nonstationary and unit root cases
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Asymptotic properties of the local Whittle estimator in the nonstationary case (d>{1/2}) are explored. For {1/2}<d\leq 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of d. For d=1, the limit distribution is mixed normal.
For d>1 and when the process has a polynomial trend of order α>{1/2}, the estimator is shown to be inconsistent and to converge in probability to unity.