An estimator for the quadratic covariation of asynchronously observed It\^o processes with noise: Asymptotic distribution theory

TL;DR

This paper develops an asymptotic distribution theory for a generalized multiscale estimator of quadratic covariation in asynchronously observed Itô processes with microstructure noise, providing a feasible CLT under regularity conditions.

Contribution

It introduces a new estimator for quadratic covariation that accounts for asynchrony and noise, with a proven asymptotic distribution and practical implementation guidance.

Findings

Feasible central limit theorem established for the estimator.

Optimal convergence rate achieved under regularity assumptions.

Impact of sampling schemes and noise on asymptotic distribution clarified.

Abstract

The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic distribution theory for a generalized multiscale estimator including a feasible central limit theorem with optimal convergence rate on convenient regularity assumptions. The inevitably remaining impact of asynchronous deterministic sampling schemes and noise corruption on the asymptotic distribution is precisely elucidated. A case study for various important examples, several generalizations of the model and an algorithm for the implementation warrant the utility of the estimation method in applications.