Estimating the Hurst parameter

Corinne Berzin (1) , José R. León (2)

1 LABSAD - Laboratoire de Statistiques et Analyse des Données
2 UCV - Universidad Central de Venezuela

Let {bH(t),t∈R} be a fractional Brownian motion with parameter 0 < H < 1. We are interested in the estimation of this parameter. To achieve this goal, we consider certain functionals of the second order increments of b H (·), using variation technics. Based on an almost-sure convergence theorem for general functionals, we single out particular functionals that allows to construct certain regression models for the parameter H. We show that this regression based estimator for H is asymptotically unbiased, consistent and that it satisfies a Central Limit Theorem.

Keywords: fractional Brownian motion; Hermite polynomials; estimation; Gaussian processes; central limit theorem

Domains: Probability [math.PR]

Corinne Berzin, José R. León. Estimating the Hurst parameter. Statistical Inference for Stochastic Processes, 2007, 10 (1), pp.49-73. ⟨10.1007/s11203-005-0059-6⟩. ⟨hal-00317829⟩