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Analyse des séries chronologiques à mémoire longue dans le domaine des ondelettes

Abstract : The theme of our work focuses on statistical process long memory, for which we propose and validate tools statistics from the wavelet analysis. In recent years these methods for estimating the memory setting became very popular. However, rigorously validating the theoretical results estimators for semiparametric models classic long memory are new (cf. the articles by E. Moulines, F. Roueff and M. Taqqu since 2007). The results we propose in this thesis are a direct extension of this work. We have proposed a test procedure for detecting changes on the generalized spectral density. In the wavelet domain, the test becomes a test of change in the variance of wavelet coefficients. We then developed an algorithm for fast computation of covariance matrix of wavelet coefficients. Two applications of this algorithm are proposed, first to estimate d and the other part to improve the test proposed in the previous chapter. Finally, we studied the robust estimators of the memory parameter in the wavelet domain, based on three estimators of the variance of wavelet coefficients at scale. The major contribution of this chapter is the central limit theorem obtained for three estimators in the context of Gaussian processes M (d).
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Submitted on : Monday, February 14, 2011 - 11:50:57 AM
Last modification on : Friday, July 31, 2020 - 10:44:07 AM
Long-term archiving on: : Saturday, December 3, 2016 - 1:37:33 PM


  • HAL Id : pastel-00565656, version 1


Olaf Kouamo. Analyse des séries chronologiques à mémoire longue dans le domaine des ondelettes. Statistiques [math.ST]. Télécom ParisTech, 2011. Français. ⟨pastel-00565656⟩



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