Testing the Eigenvalue Structure of Spot and Integrated Covariance

Dovonon, Prosper; Taamouti, Abderrahim; Williams, Julian

Abstract

For vector Itˆo semimartingale dynamics, we derive the asymptotic distributions of likelihoodratio-type test statistics for the purpose of identifying the eigenvalue structure of both integrated and spot covariance matrices estimated using high-frequency data. Unlike the existing approaches where the cross-section dimension grows to infinity, our tests do not necessarily require large crosssection and thus allow for a wide range of applications. The tests, however, are based on nonstandard asymptotic distributions with many nuisance parameters. Another contribution of this paper consists in proposing a bootstrap method to approximate these asymptotic distributions. While standard bootstrap methods focus on sampling point-wise returns, the proposed method replicates features of the asymptotic approximation of the statistics of interest that guarantee its validity. A Monte Carlo simulation study shows that the bootstrap-based test controls size and has power for even moderate size samples.

Citation

Dovonon, P., Taamouti, A., & Williams, J. (2022). Testing the Eigenvalue Structure of Spot and Integrated Covariance. Journal of Econometrics, 229(2), 363-395. https://doi.org/10.1016/j.jeconom.2021.02.006

• Journal Article Type: Article
• Acceptance Date: Feb 6, 2021
• Online Publication Date: Mar 20, 2021
• Publication Date: 2022-08
• Deposit Date: Feb 15, 2021
• Publicly Available Date: Mar 20, 2023
• Journal: Journal of Econometrics
• Print ISSN: 0304-4076
• Electronic ISSN: 1872-6895
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 229
• Issue: 2
• Article Number: 363-395
• Pages: 363-395
• DOI: https://doi.org/10.1016/j.jeconom.2021.02.006
• Public URL: https://durham-repository.worktribe.com/output/1252549