Limit Theorems for Moving Averages of Discretized Processes Plus Noise

61 Pages Posted: 2 Dec 2008

See all articles by Jean Jacod

Jean Jacod

Université Paris VI Pierre et Marie Curie

Mark Podolskij

Aarhus University - School of Economics and Management

Mathias Vetter

Ruhr University of Bochum

Date Written: December 1, 2008

Abstract

This paper presents some limit theorems for certain functionals of moving averages of semi-martingales plus noise, which are observed at high frequency. Our method generalizes the pre-averaging approach (see [13],[11]) and provides consistent estimates for various characteristics of general semi-martingales. Furthermore, we prove the associated multidimensional (stable) central limit theorems. As expected, we find central limit theorems with a convergence rate n1=4, if n is the number of observations.

Keywords: central limit theorem, high frequency observations, microstructure noise, quadratic variation, semimartingale, stable convergence

JEL Classification: C10, C13, C14

Suggested Citation

Jacod, Jean and Podolskij, Mark and Vetter, Mathias, Limit Theorems for Moving Averages of Discretized Processes Plus Noise (December 1, 2008). Available at SSRN: https://ssrn.com/abstract=1309568 or http://dx.doi.org/10.2139/ssrn.1309568

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)

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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