• Bernoulli
  • Volume 22, Number 3 (2016), 1894-1936.

Quadratic covariation estimation of an irregularly observed semimartingale with jumps and noise

Yuta Koike

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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.

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Bernoulli, Volume 22, Number 3 (2016), 1894-1936.

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

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jumps microstructure noise non-synchronous observations quadratic covariation stable limit theorem time endogeneity


Koike, Yuta. Quadratic covariation estimation of an irregularly observed semimartingale with jumps and noise. Bernoulli 22 (2016), no. 3, 1894--1936. doi:10.3150/15-BEJ714.

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