## Bernoulli

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

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 28 August 2009

https://projecteuclid.org/euclid.bj/1251463275

Digital Object Identifier
doi:10.3150/08-BEJ167

Mathematical Reviews number (MathSciNet)
MR2555193

Zentralblatt MATH identifier
1200.62131

#### Citation

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. https://projecteuclid.org/euclid.bj/1251463275

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