'Principal Component Analysis of High Frequency Data' (joint with Dacheng Xiu)
We develop a methodology to conduct principal component analysis at high frequency. The procedure involves estimation of realized eigenvalues, realized eigenvectors, and realized principal components and we provide the asymptotic distribution of these estimators. Empirically, we study the high frequency covariance structure of the constituents of the S&P 100 Index. We find that, excluding jump variation, three Brownian factors on average explain between 50 and 60% of the cross-sectional variation of stock returns, a finding that, despite the differences in methods, time periods, and length of observation, is surprisingly consistent with the well-established low frequency Fama-French common factor analysis. The explanatory power of the principal components varies over time. During crises, the first principal component becomes increasingly dominant, explaining up to 60% of the variation on its own.