Local Whittle estimation in nonstationary and unit root cases
Peter C. B. Phillips and Katsumi Shimotsu
Source: Ann. Statist. Volume 32, Number 2
(2004), 656-692.
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.
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62M10
Keywords: Discrete Fourier transform; fractional integration; long memory; nonstationarity; semiparametric estimation; trend; Whittle likelihood; unit root
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1083178942
Digital Object Identifier: doi:10.1214/009053604000000139
Mathematical Reviews number (MathSciNet): MR2060173
Zentralblatt MATH identifier: 02100809
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