Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps
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Date
2007-02-21T14:42:01Z
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Abstract
We propose a new concept of modulated bipower variation for diffusion models with
microstructure noise. We show that this method provides simple estimates for such important
quantities as integrated volatility or integrated quarticity. Under mild conditions the
consistency of modulated bipower variation is proven. Under further assumptions we prove
stable convergence of our estimates with the optimal rate n^-1/4. Moreover, we construct
estimates which are robust to finite activity jumps.
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Keywords
Bipower variation, Central limit theorem, Finite activity jumps, High-frequency data, Integrated volatility, Microstructure noise, Semimartingale theory, Subsampling