Bipower-type estimation in a noisy diffusion setting
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Date
2009-01-13T08:02:17Z
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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.
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Keywords
Bipower variation, Central limit theorem, High-frequency data, Microstructure noise, Quadratic variation, Semimartingale theory, Test for jumps