Principal Component Analysis of High Frequency Data

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