Principal Component Estimation of a Large Covariance Matrix with High-Frequency Data

Abstract

Under a large dimensional approximate factor model for asset returns, we use high frequency data to infer their covariance structure. We adapt principal component analysis (PCA) to this high frequency setting and provide an asymptotic theory that covers joint in-fill time series and diverging cross-sectional dimension asymptotics, under a variety of sparsity assumptions on the idiosyncratic covariance matrix. Empirically, we investigate the factor structure of a large port- folio of stock returns, focusing in particular on the consistency of the latent factor structure with their counterparts based on well-known observable factors in the literature.