Efficient Covariance and Correlation Matrix Measures for Multivariate Studies

34 Pages Posted: 22 Oct 2024 Last revised: 20 Jan 2025

See all articles by Zhenglyu Huang

Zhenglyu Huang

The University of Sydney

Jennifer Chan

The University of Sydney

Gareth W. Peters

University of California

Date Written: January 20, 2025

Abstract

This paper proposes efficient covariance and correlation matrix measures using high-frequency data. The proposed matrix measures are the multivariate extension of the Parkinson volatility measure that incorporates High, Low, Open and Close price information apart from the solely closing price information of the sample covariance matrices. These matrix measures facilitate the multivariate time series modelling, including the extension of volatility models such as Conditional Autoregressive Range models to multivariate settings. Model results will provide important risk measures to practitioners for portfolio or investment strategies that deal with a large number of stock assets. Through simulation studies, the proposed matrix measures are shown to perform well under heteroskedastic variance conditions and are positive semi-definite. A demonstration is provided for hypotheses testing applying the estimated variance-covariance matrices to various one and two samples tests. Results show that the proposed matrix measures outperform the sample covariance and correlation matrix measures.

Keywords: Parkinson measure, variance-covariance matrices, positive semi-definite, volatility models

Suggested Citation

Huang, Zhenglyu and Chan, Jennifer and Peters, Gareth W.,

Efficient Covariance and Correlation Matrix Measures for Multivariate Studies

(January 20, 2025). Available at SSRN: https://ssrn.com/abstract=4993702 or http://dx.doi.org/10.2139/ssrn.4993702

Zhenglyu Huang (Contact Author)

The University of Sydney ( email )

Jennifer Chan

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia
61293514873 (Phone)
2218 (Fax)

HOME PAGE: http://https://www.maths.usyd.edu.au/u/jchan/index.html

Gareth W. Peters

University of California ( email )

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