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Testing the eigenvalue structure of spot and integrated covariance

Dovonon, Prosper and Taamouti, Abderrahim and Williams, Julian (2022) 'Testing the eigenvalue structure of spot and integrated covariance.', Journal of econometrics., 229 (2). pp. 363-395.


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.

Item Type:Article
Full text:Publisher-imposed embargo until 20 March 2023.
(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives 4.0.
File format - PDF
Publisher Web site:
Publisher statement:© 2021 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:06 February 2021
Date deposited:18 February 2021
Date of first online publication:20 March 2021
Date first made open access:20 March 2023

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