Nonparametric estimation of the local Hurst function of multifractional processes

Jean-Marc Bardet (1) , Donatas Surgailis (2, 3)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 Vilnius Institute of Mathematics and Informatics
3 Institute of Mathematics and Informatics

Consistency, almost sure convergence and central limit theorems are provided for two nonparametric estimators of the local Hurst function of Gaussian multifractional processes. In the case of multifractional Brownian motions, we correct results of Coeurjolly (2005) \cite{coeur2005} and Benassi {\it et al.} (1998a) \cite{ben1998a}.

Mots clés: Gaussian process \sep central limit theorem; Nonparametric estimators; Hurst function; tangent process; multifractional Brownian motion; Gaussian process \sep central limit theorem.

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

Jean-Marc Bardet, Donatas Surgailis. Nonparametric estimation of the local Hurst function of multifractional processes. 2010. ⟨hal-00526294v1⟩