- Volume 22, Number 3 (2016), 1894-1936.
Quadratic covariation estimation of an irregularly observed semimartingale with jumps and noise
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.
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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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. https://projecteuclid.org/euclid.bj/1458133002