Application of Malliavin calculus and analysis on Wiener space to long-memory parameter estimation for non-Gaussian processes
Résumé
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 $H\in( \frac{1}{2}, 1)$. 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.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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