Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps

TL;DR

This paper extends the estimation of quadratic covariation for semimartingales to irregularly spaced and asynchronous observations, providing new asymptotic results including jumps and Poisson observation times.

Contribution

It generalizes Jacod's univariate results to the bivariate case with non-synchronous data and derives a stable CLT for the Hayashi-Yoshida estimator with jumps.

Findings

Stable central limit theorem for Hayashi-Yoshida estimator with jumps

Explicit analysis of Poisson observation times impact

Effects of idiosyncratic and simultaneous jumps on asymptotic distribution

Abstract

We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results by Jacod (2008) are generalized to the case of irregular observations. In the two-dimensional setup under non-synchronous observations, we derive a stable central limit theorem for the Hayashi-Yoshida estimator in the presence of jumps. We reveal how idiosyncratic and simultaneous jumps affect the asymptotic distribution. Observation times generated by Poisson processes are explicitly discussed.