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Testing the eigenvalue structure of spot and integrated covariance

Author

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  • Dovonon, Prosper
  • Taamouti, Abderrahim
  • Williams, Julian

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.

Suggested Citation

  • Dovonon, Prosper & Taamouti, Abderrahim & Williams, Julian, 2022. "Testing the eigenvalue structure of spot and integrated covariance," Journal of Econometrics, Elsevier, vol. 229(2), pages 363-395.
    • Handle: RePEc:eee:econom:v:229:y:2022:i:2:p:363-395
    DOI: 10.1016/j.jeconom.2021.02.006
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    More about this item

    Keywords

    Eigenvalue; Eigenvector; High frequency; Itô semimartingale; Principal components; Likelihood ratio test; Bootstrap;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G01 - Financial Economics - - General - - - Financial Crises

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