Principal Component Analysis of High Frequency Data

64 Pages Posted: 19 Aug 2015 Last revised: 22 Aug 2017

See all articles by Yacine Ait-Sahalia

Yacine Ait-Sahalia

Princeton University - Department of Economics; National Bureau of Economic Research (NBER)

Dacheng Xiu

University of Chicago - Booth School of Business

Multiple version iconThere are 2 versions of this paper

Date Written: August 21, 2017

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. The explanatory power of the high frequency principal components varies over time. 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.

Keywords: Ito Semimartingale, High Frequency, Spectral Function, Eigenvalue, Eigenvector, Principal Components, Three Factor Model

JEL Classification: C13, C14, C55, C58

Suggested Citation

Ait-Sahalia, Yacine and Xiu, Dacheng, Principal Component Analysis of High Frequency Data (August 21, 2017). Chicago Booth Research Paper No. 15-39. Available at SSRN: https://ssrn.com/abstract=2645886 or http://dx.doi.org/10.2139/ssrn.2645886

Yacine Ait-Sahalia

Princeton University - Department of Economics ( email )

Fisher Hall
Princeton, NJ 08544
United States
609-258-4015 (Phone)
609-258-5398 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Dacheng Xiu (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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