Limiting Spectral Distribution of High-dimensional Hayashi-Yoshida Estimator of Integrated Covariance Matrix

TL;DR

This paper analyzes the spectral properties of the high-dimensional Hayashi-Yoshida estimator for integrated covariance matrices, revealing its limitations and establishing theoretical connections to the true covariance spectrum in high dimensions.

Contribution

It provides a theoretical analysis of the estimator's spectral distribution in high dimensions and demonstrates its practical implications through simulations and real data.

Findings

Spectral distribution converges to a limit related to the true covariance spectrum.

The estimator becomes inconsistent in high dimensions without adjustments.

Simulation and real data validate the theoretical results.

Abstract

In this paper, the estimation of the Integrated Covariance matrix from high-frequency data, for high dimensional stock price process, is considered. The Hayashi-Yoshida covolatility estimator is an improvement over Realized covolatility for asynchronous data and works well in low dimensions. However it becomes inconsistent and unreliable in the high dimensional situation. We study the bulk spectrum of this matrix and establish its connection to the spectrum of the true covariance matrix in the limiting case where the dimension goes to infinity. The results are illustrated with simulation studies in finite, but high, dimensional cases. An application to real data with tick-by-tick data on 50 stocks is presented.