Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

Jean-Marc Bardet (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a multidimensional central limit theorem for this estimator are established. Similar results are obtained for a refinement of the generalized quadratic variations (QV) estimator. The example of the multifractional Brownian motion is studied in detail. A simulation study is included showing that the IR-estimator is more accurate than the QV-estimator.

Mots clés: Théorèmes limite; Estimation non-paramétrique; Mouvement brownien fractionnaire; Mouvement brownien multifractionnaire; Théorèmes limite.

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

Jean-Marc Bardet. Nonparametric estimation of the local Hurst function of multifractional Gaussian processes. Colloque Franco-Roumain de Mathématiques Appliquées, Aug 2012, Bucarest, Romania. ⟨hal-00728913⟩