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INFERENCE FOR THE JUMP PART OF QUADRATIC VARIATION OF ITÔ SEMIMARTINGALES

Published online by Cambridge University Press:  18 August 2009

Almut E.D. Veraart
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Abstract

Recent research has focused on modeling asset prices by Itô semimartingales. In such a modeling framework, the quadratic variation consists of a continuous and a jump component. This paper is about inference on the jump part of the quadratic variation, which can be estimated by the difference of realized variance and realized multipower variation. The main contribution of this paper is twofold. First, it provides a bivariate asymptotic limit theory for realized variance and realized multipower variation in the presence of jumps. Second, this paper presents new, consistent estimators for the jump part of the asymptotic variance of the estimation bias. Eventually, this leads to a feasible asymptotic theory that is applicable in practice. Finally, Monte Carlo studies reveal a good finite sample performance of the proposed feasible limit theory.

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 2 , April 2010 , pp. 331 - 368
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

This paper is a revised part of my D.Phil. thesis and, therefore, I wish to thank my supervisors Neil Shephard and Matthias Winkel for their guidance and support throughout this project. Furthermore, I am grateful to Ole Barndorff–Nielsen, Mark Podolskij, and two anonymous referees for constructive comments on an earlier draft of this article. Financial support by the Rhodes Trust and by the Center for Research in Econometric Analysis of Time Series (CREATES), funded by the Danish National Research Foundation, is gratefully acknowledged.

References

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