Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9

CREATES Research Paper 2007-43

32 Pages Posted: 24 Jun 2008 Last revised: 20 May 2010

See all articles by Jean Jacod

Jean Jacod

Université Paris VI Pierre et Marie Curie

Yingying Li

Hong Kong University of Science & Technology (HKUST), Dept of ISOM and Dept of Finance; Hong Kong University of Science & Technology (HKUST) - Department of Information Systems, Business Statistics and Operations Management; Hong Kong University of Science & Technology (HKUST) - Department of Finance

Per A. Mykland

University of Chicago - Department of Statistics

Mark Podolskij

Aarhus University - School of Economics and Management

Mathias Vetter

Ruhr University of Bochum

Date Written: December 10, 2007

Abstract

This paper presents a generalized pre-averaging approach for estimating the integrated volatility. This approach also provides consistent estimators of other powers of volatility - in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the integrated volatility. We show that our approach, which possess an intuitive transparency, can generate rate optimal estimators (with convergence rate n-1/4).

Keywords: consistency, continuity, discrete observation, Itý process, leverage effect, pre-averaging, quarticity, realized volatility, stable convergence

JEL Classification: C10, C13, C14

Suggested Citation

Jacod, Jean and Li, Yingying and Mykland, Per A. and Podolskij, Mark and Vetter, Mathias, Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9 (December 10, 2007). CREATES Research Paper 2007-43. Available at SSRN: https://ssrn.com/abstract=1150685 or http://dx.doi.org/10.2139/ssrn.1150685

Jean Jacod (Contact Author)

Université Paris VI Pierre et Marie Curie ( email )

4, Place Jussieu, B.P. 169
Laboratoire de Probabilites
F-75252-Paris Cedex 05
France
01 44 27 53 21 (Phone)

Yingying Li

Hong Kong University of Science & Technology (HKUST), Dept of ISOM and Dept of Finance ( email )

Clear Water Bay, Kowloon
Hong Kong

Hong Kong University of Science & Technology (HKUST) - Department of Information Systems, Business Statistics and Operations Management ( email )

Clear Water Bay
Kowloon
Hong Kong

Hong Kong University of Science & Technology (HKUST) - Department of Finance ( email )

Clear Water Bay, Kowloon
Hong Kong

Per A. Mykland

University of Chicago - Department of Statistics ( email )

Chicago, IL 60637-1514
United States
773-702-8044 (Phone)

Mark Podolskij

Aarhus University - School of Economics and Management ( email )

Building 350
DK-8000 Aarhus C
Denmark

Mathias Vetter

Ruhr University of Bochum ( email )

Universitätsstraße 150
Bochum, NRW 44780
Germany

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