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April 2004 Local Whittle estimation in nonstationary and unit root cases
Peter C. B. Phillips, Katsumi Shimotsu
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Ann. Statist. 32(2): 656-692 (April 2004). DOI: 10.1214/009053604000000139


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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Peter C. B. Phillips. Katsumi Shimotsu. "Local Whittle estimation in nonstationary and unit root cases." Ann. Statist. 32 (2) 656 - 692, April 2004.


Published: April 2004
First available in Project Euclid: 28 April 2004

zbMATH: 1091.62084
MathSciNet: MR2060173
Digital Object Identifier: 10.1214/009053604000000139

Primary: 62M10

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

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 2 • April 2004
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