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Principal Component Analysis of High-Frequency Data

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  • Yacine Aït-Sahalia
  • Dacheng Xiu

Abstract

We develop the necessary methodology to conduct principal component analysis at high frequency. We construct estimators of realized eigenvalues, eigenvectors, and principal components, and provide the asymptotic distribution of these estimators. Empirically, we study the high-frequency covariance structure of the constituents of the S&P 100 Index using as little as one week of high-frequency data at a time, and examines whether it is compatible with the evidence accumulated over decades of lower frequency returns. We find a surprising consistency between the low- and high-frequency structures. During the recent financial crisis, the first principal component becomes increasingly dominant, explaining up to 60% of the variation on its own, while the second principal component drives the common variation of financial sector stocks. Supplementary materials for this article are available online.

Suggested Citation

  • Yacine Aït-Sahalia & Dacheng Xiu, 2019. "Principal Component Analysis of High-Frequency Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 287-303, January.
    • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:525:p:287-303
    DOI: 10.1080/01621459.2017.1401542
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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G01 - Financial Economics - - General - - - Financial Crises

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