Testing the eigenvalue structure of spot and integrated covariance

Prosper Dovonon, Abderrahim Taamouti and Julian Williams

Journal of Econometrics, 2022, vol. 229, issue 2, 363-395

Abstract: 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.

Keywords: Eigenvalue; Eigenvector; High frequency; Itô semimartingale; Principal components; Likelihood ratio test; Bootstrap (search for similar items in EconPapers)
JEL-codes: C13 C14 C15 C58 G01 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:229:y:2022:i:2:p:363-395

DOI: 10.1016/j.jeconom.2021.02.006

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