  Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$
of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a
one-dimensional positive diffusion process independent of the Brownian motion
$B$. For both the drift and the diffusion coefficient of the unobserved
diffusion $V$, we propose nonparametric least square estimators, and provide
bounds for theirrisk. Estimators are chosen among a collection of functions
belonging to a finite dimensional space whose dimension is selected by a data
driven procedure. Implementation on simulated data illustrates how the method
works.
