Estimation of integrated quadratic covariation with endogenous sampling times

TL;DR

This paper develops a new model for estimating high-frequency covariance of assets observed asynchronously, accounting for endogenous sampling times, and introduces bias correction and standard error estimation methods.

Contribution

It introduces the HBT model for endogenous sampling times and derives a bias-corrected HY estimator with standard error estimation.

Findings

Central limit theorem established for HY estimator under HBT

Asymptotic bias identified and corrected

Consistent estimator of standard error provided

Abstract

When estimating high-frequency covariance (quadratic covariation) of two arbitrary assets observed asynchronously, simple assumptions, such as independence, are usually imposed on the relationship between the prices process and the observation times. In this paper, we introduce a general endogenous two-dimensional nonparametric model. Because an observation is generated whenever an auxiliary process called observation time process hits one of the two boundary processes, it is called the hitting boundary process with time process (HBT) model. We establish a central limit theorem for the Hayashi-Yoshida (HY) estimator under HBT in the case where the price process and the observation price process follow a continuous Ito process. We obtain an asymptotic bias. We provide an estimator of the latter as well as a bias-corrected HY estimator of the high-frequency covariance. In addition, we give a consistent estimator of the associated standard error.