Asymptotics of Asynchronicity

TL;DR

This paper investigates the asymptotic behavior of the Hayashi-Yoshida estimator for quadratic covariation of continuous semimartingales observed asynchronously, providing new insights and a stable CLT under high-frequency sampling.

Contribution

It introduces a novel iterative synchronization algorithm and derives a feasible stable central limit theorem for asynchronous high-frequency data, explicitly characterizing asymptotic variances.

Findings

Explicit formulas for asymptotic covariations of times under Poisson sampling

A stable CLT for the Hayashi-Yoshida estimator in high-frequency asymptotics

Insights into how non-synchronous observation schemes affect estimator variance

Abstract

In this article we focus on estimating the quadratic covariation of continuous semimartingales from discrete observations that take place at asynchronous observation times. The Hayashi-Yoshida estimator serves as synchronized realized covolatility for that we give our own distinct illustration based on an iterative synchronization algorithm. We consider high-frequency asymptotics and prove a feasible stable central limit theorem. The characteristics of non-synchronous observation schemes affecting the asymptotic variance are captured by a notion of asymptotic covariations of times. These are precisely illuminated and explicitly deduced for the important case of independent time-homogeneous Poisson sampling.