Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/36601
Authors: 
Podolskij, Mark
Vetter, Mathias
Year of Publication: 
2008
Series/Report no.: 
Technical Report // Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund 2008,24
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.
Subjects: 
Bipower Variation
Central Limit Theorem
High-Frequency Data
Microstructure Noise
Quadratic Variation
Semimartingale Theory
Test for Jumps
Document Type: 
Working Paper

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