Application of Malliavin calculus and analysis on Wiener space to long-memory parameter estimation for non-Gaussian processes

Alexandra Chronopoulou (1) , Ciprian A. Tudor (2, 3) , Frederi Viens (1)

1 Department of Statistics [West Lafayette]
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 CES - Centre d'économie de la Sorbonne

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.

Domains: Probability [math.PR]

Alexandra Chronopoulou, Ciprian A. Tudor, Frederi Viens. Application of Malliavin calculus and analysis on Wiener space to long-memory parameter estimation for non-Gaussian processes. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2009, 347 (11-12), pp.663-666. ⟨10.1016/j.crma.2009.03.026⟩. ⟨hal-00436527⟩