Using multiple Wiener–Itô stochastic integrals and Malliavin calculus we study the rescaled quadratic variations of a general Hermite process of order q with long-memory (Hurst) parameter . We apply our results to the construction of a strongly consistent estimator for H. It is shown that the estimator is asymptotically non-normal, and converges in the mean-square, after normalization, to a standard Rosenblatt random variable.
Nous servant des intégrales multiples de Wiener–Itô et du calcul de Malliavin, nous étudions la variation quadratique renormalisée d'un processus de Hermite général d'ordre q avec paramètre de mémoire longue . Nous appliquons nos résultats à la construction d'un estimateur fortement consistent pour H. Il est démontré que l'estimateur est asymptotiquement non-normal, et converge en moyenne de carrés, après normalisation, vers une variable aléatoire de Rosenblatt standard.
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@article{CRMATH_2009__347_11-12_663_0,
author = {Chronopoulou, Alexandra and Tudor, Ciprian A. and Viens, Frederi G.},
title = {Application of {Malliavin} calculus to long-memory parameter estimation for {non-Gaussian} processes},
journal = {Comptes Rendus. Math\'ematique},
pages = {663--666},
publisher = {Elsevier},
volume = {347},
number = {11-12},
year = {2009},
doi = {10.1016/j.crma.2009.03.026},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.03.026/}
}
TY - JOUR AU - Chronopoulou, Alexandra AU - Tudor, Ciprian A. AU - Viens, Frederi G. TI - Application of Malliavin calculus to long-memory parameter estimation for non-Gaussian processes JO - Comptes Rendus. Mathématique PY - 2009 SP - 663 EP - 666 VL - 347 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.03.026/ DO - 10.1016/j.crma.2009.03.026 LA - en ID - CRMATH_2009__347_11-12_663_0 ER -
%0 Journal Article %A Chronopoulou, Alexandra %A Tudor, Ciprian A. %A Viens, Frederi G. %T Application of Malliavin calculus to long-memory parameter estimation for non-Gaussian processes %J Comptes Rendus. Mathématique %D 2009 %P 663-666 %V 347 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.03.026/ %R 10.1016/j.crma.2009.03.026 %G en %F CRMATH_2009__347_11-12_663_0
Chronopoulou, Alexandra; Tudor, Ciprian A.; Viens, Frederi G. Application of Malliavin calculus to long-memory parameter estimation for non-Gaussian processes. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 663-666. doi : 10.1016/j.crma.2009.03.026. http://www.numdam.org/articles/10.1016/j.crma.2009.03.026/
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