A Wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series

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dc.creatorMoulines, Eric
dc.creatorRoueff, François
dc.creatorTaqqu, Murad S.
dc.date2006-01-04
dc.date2008-08-18
dc.date.accessioned2026-07-07T09:56:55Z
dc.date.available2026-07-07T09:56:55Z
dc.descriptionWe consider a time series $X=\{X_k, k\in\mathbb{Z}\}$ with memory parameter $d\in\mathbb{R}$. 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 $d$. 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.
dc.identifierhttps://arxiv.org/abs/math/0601070
dc.identifierhttp://arxiv.org/abs/math/0601070
dc.identifierThe Annals of Statistics 36, 4 (2008) 1925-1956
dc.identifierdoi:10.1214/07-AOS527
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167153
dc.subjectStatistics Theory
dc.subject62M15, 62M10, 62G05 (Primary); 62G20, 60G18 (Secondary)
dc.titleA Wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series
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