Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data

2026-02-23

AI Summary

This study addresses the challenges posed by market microstructure noise and asynchronous trading in high-frequency financial data by proposing a post-hoc covariance estimator based on pre-averaging techniques. The method obviates the need for price alignment and simultaneously achieves robustness to noise and compatibility with irregular, non-synchronous observations. It can be flexibly configured either to attain the optimal convergence rate or to ensure the positive semi-definiteness of the resulting covariance matrix. Theoretical analysis demonstrates that the proposed pre-averaged realized covariance estimator possesses optimal asymptotic properties. Extensive simulations confirm its superior finite-sample performance, and empirical applications to real high-frequency equity data illustrate its practical effectiveness.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an asymptotic theory for this new estimator, which can be configured to possess an optimal convergence rate or to ensure positive semi-definite covariance matrix estimates. We also derive a noise-robust Hayashi-Yoshida estimator that can be implemented on the original data without prior alignment of prices. We uncover the finite sample properties of our estimators with simulations and illustrate their practical use on high-frequency equity data.

Problem

• ex-post covariance
• microstructure noise
• non-synchronous data
• high-frequency data
• covariance estimation

Innovation

• pre-averaging
• ex-post covariance
• microstructure noise
• non-synchronous data
• Hayashi-Yoshida estimator