The Annals of Statistics

A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series

E. Moulines, F. Roueff, and M. S. Taqqu

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We consider a time series X={Xk, k∈ℤ} with memory parameter d0∈ℝ. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the “local Whittle wavelet estimator” of the memory parameter d0. This is a wavelet-based semiparametric pseudo-likelihood maximum method estimator. The estimator may depend on a given finite range of scales or on a range which becomes infinite with the sample size. We show that the estimator is consistent and rate optimal if X is a linear process, and is asymptotically normal if X is Gaussian.

Article information

Ann. Statist. Volume 36, Number 4 (2008), 1925-1956.

First available in Project Euclid: 16 July 2008

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Zentralblatt MATH identifier

Primary: 62M15: Spectral analysis 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62G05: Estimation
Secondary: 62G20: Asymptotic properties 60G18: Self-similar processes

Long memory semiparametric estimation wavelet analysis


Moulines, E.; Roueff, F.; Taqqu, M. S. A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series. The Annals of Statistics 36 (2008), no. 4, 1925--1956. doi:10.1214/07-AOS527.

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