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Local Whittle Estimation In Nonstationary And Unit Root Cases, Katsumi Shimotsu, Peter C.B. Phillips

Cowles Foundation Discussion Papers

Asymptotic properties of the local Whittle estimator in the nonstationary case (d > 1/2) are explored. For 1/2 < d < 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 linear trend, the estimator is shown to be inconsistent and to converge in probability to unity.