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August 2008 A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series
E. Moulines, F. Roueff, M. S. Taqqu
Ann. Statist. 36(4): 1925-1956 (August 2008). DOI: 10.1214/07-AOS527

Abstract

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.

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E. Moulines. F. Roueff. M. S. Taqqu. "A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series." Ann. Statist. 36 (4) 1925 - 1956, August 2008. https://doi.org/10.1214/07-AOS527

Information

Published: August 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1142.62062
MathSciNet: MR2435460
Digital Object Identifier: 10.1214/07-AOS527

Subjects:
Primary: 62G05 , 62M10 , 62M15
Secondary: 60G18 , 62G20

Keywords: long memory , Semiparametric estimation , wavelet analysis

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 4 • August 2008
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