A Geometric Framework for Covariance Dynamics

Han, Chulwoo; Park, Frank C.

Abstract

Employing methods of differential geometry, we propose a new framework for covariance dynamics modeling. Our approach respects the intrinsic geometric properties of the space of covariance matrices and allows their natural evolution. We develop covariance models that exploit either asset returns or realized covariances and propose a new estimation method that minimizes the length of the geodesic between the forecast and the realization. The geodesic length is equivalent to the Fisher information metric under the Gaussian assumption and is deemed a proper measure of similarity between two covariance matrices. Empirical studies involving three data samples and various performance metrics suggest that our models outperform existing ones.

Citation

Han, C., & Park, F. C. (2022). A Geometric Framework for Covariance Dynamics. Journal of Banking and Finance, 134, Article 106319. https://doi.org/10.1016/j.jbankfin.2021.106319

• Journal Article Type: Article
• Acceptance Date: Sep 19, 2021
• Online Publication Date: Sep 20, 2021
• Publication Date: 2022-01
• Deposit Date: Sep 21, 2021
• Publicly Available Date: Mar 20, 2023
• Journal: Journal of Banking and Finance
• Print ISSN: 0378-4266
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 134
• Article Number: 106319
• DOI: https://doi.org/10.1016/j.jbankfin.2021.106319
• Public URL: https://durham-repository.worktribe.com/output/1240752