Podolskij, MarkVetter, Mathias2009-01-132009-01-132009-01-13http://hdl.handle.net/2003/25990http://dx.doi.org/10.17877/DE290R-14128We consider a new class of estimators for volatility functionals in the setting of frequently observed Ito diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence of microstructure noise and are closely related to the original concept of bipower variation in the no-noise case. We show that this approach provides efficient estimators for a large class of integrated powers of volatility and prove the associated (stable) central limit theorems. In a more general Ito semimartingale framework this method can be used to define both estimators for the entire quadratic variation of the underlying process and jump-robust estimators which are consistent for various functionals of volatility. As a by-product we obtain a simple test for the presence of jumps in the underlying semimartingale.enBipower variationCentral limit theoremHigh-frequency dataMicrostructure noiseQuadratic variationSemimartingale theoryTest for jumps004Text