Local Whittle Estimation in Nonstationary and Unit Root Cases

Asymptotic properties of the local Whittle estimator in the nonstationary case (d \u3e 1/2) are explored. For 1/2 \u3c d \u3c 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 \u3e 1 and when the process has a linear trend, the estimator is shown to be inconsistent and to converge in probability to unity