Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps

37 Pages Posted: 8 Dec 2006

See all articles by Mark Podolskij

Mark Podolskij

University of Heidelberg - Institute of Applied Mathematics

Mathias Vetter

Ruhr University of Bochum

Margit Sommer

School of Economics and Management; School of Economics and Management, University of Aarhus; CREATES Research Papers

Date Written: September 19, 2007

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.

Keywords: Bipower Variation, Central Limit Theorem, Finite Activity Jumps, High-Frequency Data, Integrated Volatility, Microstructure Noise, Semimartingale Theory, Subsampling

JEL Classification: C10, C13, C14

Suggested Citation

Podolskij, Mark and Vetter, Mathias and Sommer, Margit and Sommer, Margit, Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps (September 19, 2007). Available at SSRN: https://ssrn.com/abstract=950344 or http://dx.doi.org/10.2139/ssrn.950344

Mark Podolskij (Contact Author)

University of Heidelberg - Institute of Applied Mathematics ( email )

Grabengasse 1
Heidelberg, 69117
Germany
00496221546276 (Phone)

Mathias Vetter

Ruhr University of Bochum ( email )

Universitätsstraße 150
Bochum, NRW 44780
Germany

Margit Sommer

School of Economics and Management ( email )

Building 350
DK-8000 Aarhus C
Denmark

School of Economics and Management, University of Aarhus ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

CREATES Research Papers ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

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