Testing the eigenvalue structure of spot and integrated covariance?

Dovonon, Prosper, Taamouti, Abderrahim ORCID: 0000-0002-1360-8803 and Williams, Julian
(2022) Testing the eigenvalue structure of spot and integrated covariance? JOURNAL OF ECONOMETRICS, 229 (2). pp. 363-395.

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For vector Itô semimartingale dynamics, we derive the asymptotic distributions of likelihood-ratio-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 cross-section and thus allow for a wide range of applications. The tests, however, are based on non-standard 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
Uncontrolled Keywords: Bootstrap, Eigenvalue, Eigenvector, High frequency, It? semimartingale, Likelihood ratio test, Principal components
Depositing User: Symplectic Admin
Date Deposited: 12 Dec 2022 09:55
Last Modified: 28 Oct 2023 21:53
DOI: 10.1016/j.jeconom.2021.02.006
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3166593