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

TL;DR

This paper establishes a central limit theorem for a pre-averaged realized covariance estimator of a semimartingale with jumps and noise, accounting for irregular observation times and their impact on estimation accuracy.

Contribution

It introduces a new asymptotic distribution result for quadratic covariation estimation under complex observation schemes with noise and jumps.

Findings

Observation times affect asymptotic distribution only through frequency and noise covariance.

The estimator remains consistent despite irregular, non-synchronous observations.

The results differ from pure semimartingale cases, highlighting the impact of noise and jumps.

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.