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August 2016 Quadratic covariation estimation of an irregularly observed semimartingale with jumps and noise
Yuta Koike
Bernoulli 22(3): 1894-1936 (August 2016). DOI: 10.3150/15-BEJ714

Abstract

This paper presents a central limit theorem for a pre-averaged version of the realized covariance estimator for the quadratic covariation of a discretely observed semimartingale with noise. The semimartingale possibly has jumps, while the observation times show irregularity, non-synchronicity, and some dependence on the observed process. It is shown that the observation times’ effect on the asymptotic distribution of the estimator is only through two characteristics: the observation frequency and the covariance structure of the noise. This is completely different from the case of the realized covariance in a pure semimartingale setting.

Citation

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Yuta Koike. "Quadratic covariation estimation of an irregularly observed semimartingale with jumps and noise." Bernoulli 22 (3) 1894 - 1936, August 2016. https://doi.org/10.3150/15-BEJ714

Information

Received: 1 August 2014; Revised: 1 January 2015; Published: August 2016
First available in Project Euclid: 16 March 2016

zbMATH: 1342.60033
MathSciNet: MR3474836
Digital Object Identifier: 10.3150/15-BEJ714

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

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Vol.22 • No. 3 • August 2016
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