Bipower-type estimation in a noisy diffusion setting

Mark Podolskij () and Mathias Vetter

No 2008,24, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

Abstract: We consider a new class of estimators for volatility functionals in the setting of frequently observed It¯o 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 It¯o 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.

Keywords: Bipower Variation; Central Limit Theorem; High-Frequency Data; Microstructure Noise; Quadratic Variation; Semimartingale Theory; Test for Jumps (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Bipower-type estimation in a noisy diffusion setting (2009)
Working Paper: Bipower-type estimation in a noisy diffusion setting (2008)
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