Principal Component Analysis of High-Frequency Data

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 st...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 114; no. 525; pp. 287 - 303
Main Authors: Aït-Sahalia, Yacine, Xiu, Dacheng
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 02.01.2019
Taylor & Francis Group,LLC
Taylor & Francis Ltd
Subjects:
Analysis of covariance
Covariance
economic crises
Economic crisis
Eigenvalue
Eigenvalues
Eigenvector
Eigenvectors
equations
Estimators
High frequency
Itô semimartingale
principal component analysis
Principal components
Principal components analysis
Regression analysis
Securities markets
Spectral function
Statistical methods
Statistics
Stocks
Theory and Methods
ISSN:0162-1459, 1537-274X, 1537-274X
Online Access:Get full text
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Summary: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.
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2017.1401542