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A Geometric Framework for Covariance Dynamics

Han, Chulwoo; Park, Frank C.

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Authors

Chulwoo Han

Frank C. Park



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

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