Large-Dimensional Factor Modeling Based on High-Frequency Observations

Abstract

This paper develops a statistical theory to estimate an unknown factor structure based on financial high-frequency data. We derive an estimator for the number of factors and consistent and asymptotically mixed-normal estimators of the loadings and factors under the assumption of a large number of cross-sectional and high-frequency observations. The estimation approach can separate factors for continuous and rare jump risk. The estimators for the loadings and factors are based on the principal component analysis of the quadratic covariation matrix. The estimator for the number of factors uses a perturbed eigenvalue ratio statistic. In an empirical analysis of the S&P 500 firms we estimate four stable continuous systematic factors, which can be approximated very well by a market and industry portfolios. Jump factors are different from the continuous factors.

Keywords: Systematic risk, High-dimensional data, High-frequency data, Latent factor model, PCA, Jumps, Semimartingales, Approximate factor model, Number of factors

JEL Classification: C14, C38, C55, C58