Principal Component Analysis of High-Frequency Data
本文开发了高频数据下主成分分析的方法，估计了实现特征值、特征向量和主成分，并给出渐近分布。实证用一周高频数据研究标普100成分股的协方差结构，发现低频与高频结构一致，金融危机中第一主成分解释高达60%的变异。
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.