Estimating the Hurst parameter

International audienceLet {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