On covariation estimation for multivariate continuous Itô semimartingales with noise in non-synchronous observation schemes

2026-02-23

AI Summary

This work proposes a robust, time-synchronization-free estimator for the integrated covariance matrix of multivariate continuous Itô semimartingales observed asynchronously at high frequency under market microstructure noise. The method combines local averaging with a Hayashi–Yoshida-type estimator and employs a blocking technique to circumvent conventional synchronization schemes such as previous-tick or refreshing times. Theoretical analysis establishes a central limit theorem for the proposed estimator and provides a feasible asymptotic inference framework, confirming its asymptotic normality. Simulation studies demonstrate superior finite-sample performance, highlighting its practical effectiveness in realistic settings with noisy, irregularly spaced observations.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: The sharing economy

Abstract

This paper presents a Hayashi-Yoshida type estimator for the covariation matrix of continuous Itô semimartingales observed with noise. The coordinates of the multivariate process are assumed to be observed at highly frequent non-synchronous points. The estimator of the covariation matrix is designed via a certain combination of the local averages and the Hayashi-Yoshida estimator. Our method does not require any synchronization of the observation scheme (as e.g. previous tick method or refreshing time method) and it is robust to some dependence structure of the noise process. We show the associated central limit theorem for the proposed estimator and provide a feasible asymptotic result. Our proofs are based on a blocking technique and a stable convergence theorem for semimartingales. Finally, we show simulation results for the proposed estimator to illustrate its finite sample properties.

Problem

• covariation estimation
• Itô semimartingales
• observation noise
• non-synchronous observations
• multivariate processes

Innovation

• Hayashi-Yoshida estimator
• non-synchronous observations
• measurement noise
• covariation estimation
• Itô semimartingales