  We propose a new concept of modulated bipower variation for diffusion models
with microstructure noise. We show that this method provides simple estimates
for such important quantities as integrated volatility or integrated
quarticity. Under mild conditions the consistency of modulated bipower
variation is proven. Under further assumptions we prove stable convergence of
our estimates with the optimal rate $n^{-{1}/{4}}$. Moreover, we construct
estimates which are robust to finite activity jumps.
