Authors: Podolskij, Mark
Vetter, Mathias
Title: Bipower-type estimation in a noisy diffusion setting
Language (ISO): en
Abstract: We 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.
Subject Headings: Bipower variation
Central limit theorem
High-frequency data
Microstructure noise
Quadratic variation
Semimartingale theory
Test for jumps
Issue Date: 2009-01-13T08:02:17Z
Appears in Collections:Sonderforschungsbereich (SFB) 475

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