This paper develops a statistical theory to estimate an unknown factor structure based on financial high-frequency data. I derive a new estimator for the number of factors and derive 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 normal "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. The results are obtained under general conditions, that allow for a very rich class of stochastic processes and for serial and cross-sectional correlation in the idiosyncratic components.
Markus Pelger is an Assistant Professor at the Management Science & Engineering Department at Stanford University. His research interests are in statistics, financial econometrics, asset pricing and risk management. Markus received his Ph.D. in Economics from the University of California, Berkeley. He has a Diplom in Mathematics and a Diplom in Economics from the University of Bonn in Germany.