Theoremes limites pour les fonctionnelles du periodogramme

Abstract : The periodogram is the main tool for time series analysis in the spectral domain. Some of its (asymptotic) properties are well known, for short or long range dependent stationnary processes. Our work focussed on the extension of some of those results to an non-Gaussian framework. We considered linear processes, for which we showed first that non-linear functionals of the periodogram satisfy a central limit principle, using moment methods and the Bartlett decomposition. In most cases, this (yet heavy) technique does not yield any control on the moments of the considered functional. We then achieve moment control through the proof of the validity of the Edgeworth expansion for the Fourier transform of the observation in short and long range contexts.
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Mathematics. Ecole nationale supérieure des telecommunications - ENST, 2000. French


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Submitted on : Tuesday, February 26, 2002 - 1:19:09 PM
Last modification on : Wednesday, January 4, 2006 - 11:00:08 PM

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  • HAL Id : tel-00001139, version 1

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Gilles Fay. Theoremes limites pour les fonctionnelles du periodogramme. Mathematics. Ecole nationale supérieure des telecommunications - ENST, 2000. French. <tel-00001139>

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