Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps

Mark Podolskij, Mathias Vetter
2009 Bernoulli  
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.
doi:10.3150/08-bej167 fatcat:wozqudceyvhxxpjmyp5mmp3r6i