The Annals of Statistics

Exact local Whittle estimation of fractional integration

Katsumi Shimotsu and Peter C. B. Phillips

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An exact form of the local Whittle likelihood is studied with the intent of developing a general-purpose estimation procedure for the memory parameter (d) that does not rely on tapering or differencing prefilters. The resulting exact local Whittle estimator is shown to be consistent and to have the same $N(0,\frac{1}{4})$ limit distribution for all values of d if the optimization covers an interval of width less than $\frac{9}{2}$ and the initial value of the process is known.

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Ann. Statist. Volume 33, Number 4 (2005), 1890-1933.

First available: 5 August 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


Shimotsu, Katsumi; Phillips, Peter C. B. Exact local Whittle estimation of fractional integration. The Annals of Statistics 33 (2005), no. 4, 1890--1933. doi:10.1214/009053605000000309.

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