On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter

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dc.creatorMoulines, Eric
dc.creatorRoueff, François
dc.creatorTaqqu, Murad
dc.date2005-12-29
dc.date2006-08-17
dc.date.accessioned2026-07-07T08:07:26Z
dc.date.available2026-07-07T08:07:26Z
dc.descriptionIn the recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semi-parametric asymptotic theory, comparable to the one developed for Fourier methods, is still missing. In this contribution, we adapt the classical semi-parametric framework introduced by Robinson and his co-authors for estimating the memory parameter of a (possibly) non-stationary process. As an application, we obtain minimax upper bounds for the log-scale regression estimator of the memory parameter for a Gaussian process and we derive an explicit expression of its variance.
dc.descriptionto appear in the Journal of Time Series Analysis
dc.identifierhttps://arxiv.org/abs/math/0512635
dc.identifierhttp://arxiv.org/abs/math/0512635
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130940
dc.subjectStatistics Theory
dc.subjectAMS Keywords: 62M10, 60G18 Secondary: 62M15
dc.titleOn the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter
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