• Bernoulli
  • Volume 15, Number 3 (2009), 634-658.

Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps

Mark Podolskij and Mathias Vetter

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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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Bernoulli, Volume 15, Number 3 (2009), 634-658.

First available in Project Euclid: 28 August 2009

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bipower variation central limit theorem finite activity jumps high-frequency data integrated volatility microstructure noise semimartingale theory subsampling


Podolskij, Mark; Vetter, Mathias. Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps. Bernoulli 15 (2009), no. 3, 634--658. doi:10.3150/08-BEJ167.

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