Estimation of the volatility persistence in a discretely observed diffusion model

We consider the stochastic volatility model with B a Brownian motion and [sigma] of the form where WH is a fractional Brownian motion, independent of the driving Brownian motion B, with Hurst parameter H>=1/2. This model allows for persistence in the volatility [sigma]. The parameter of interest is H. The functions [Phi], a and f are treated as nuisance parameters and [xi]0 is a random initial condition. For a fixed objective time T, we construct from discrete data Yi/n,i=0,...,nT, a wavelet based estimator of H, inspired by adaptive estimation of quadratic functionals. We show that the accuracy of our estimator is n-1/(4H+2) and that this rate is optimal in a minimax sense.