The Annals of Statistics

Local Whittle estimation in nonstationary and unit root cases

Peter C. B. Phillips and Katsumi Shimotsu

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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.

Article information

Ann. Statist., Volume 32, Number 2 (2004), 656-692.

First available in Project Euclid: 28 April 2004

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Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Discrete Fourier transform fractional integration long memory nonstationarity semiparametric estimation trend Whittle likelihood unit root


Phillips, Peter C. B.; Shimotsu, Katsumi. Local Whittle estimation in nonstationary and unit root cases. Ann. Statist. 32 (2004), no. 2, 656--692. doi:10.1214/009053604000000139.

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