Local Whittle estimation in nonstationary and unit root cases

The Annals of Statistics · 2004 · Volume 32 · Issue 2

Abstract

Asymptotic properties of the local Whittle estimator in the nonstationary case (d>½) are explored. For ½<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 polynomial trend of order α>½, the estimator is shown to be inconsistent and to converge in probability to unity.

Keywords

62M10, discrete Fourier transform, fractional integration, long memory, nonstationarity, Semiparametric estimation, trend, unit root, Whittle likelihood

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