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Testing the Eigenvalue Structure of Spot and Integrated Covariance

Dovonon, Prosper; Taamouti, Abderrahim; Williams, Julian

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Authors

Prosper Dovonon



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 28, 2024
Journal Journal of Econometrics
Print ISSN 0304-4076
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

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