Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process

Jean-Marc Bardet (1) , Ciprian A. Tudor (2)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 LPP - Laboratoire Paul Painlevé - UMR 8524

The purpose of this paper is to estimate the self-similarity index of the Rosenblatt process by using the Whittle estimator. Via chaos expansion into multiple stochastic integrals, we establish a non-central limit theorem satisfied by this estimator. We illustrate our results by numerical simulations.

Mots clés: Malliavin calculus; Whittle estimator; Rosenblatt process; long-memory process; non-central limit theorem; Malliavin calculus.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-Marc Bardet, Ciprian A. Tudor. Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process. Journal of Multivariate Analysis, 2014, 131, pp.1-16. ⟨10.1016/j.jmva.2014.06.012⟩. ⟨hal-00793904⟩