Efficient Covariance and Correlation Matrix Measures for Multivariate Studies
34 Pages Posted: 22 Oct 2024 Last revised: 20 Jan 2025
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: Suggested Citation
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