Principal Component Analysis of High Frequency Data

We thank Hristo Sendov for valuable discussions on eigenvalues and spectral functions. In addition, we benefited much from comments by Torben Andersen, Tim Bollerslev, Oleg Bondarenko, Marine Carrasco, Gary Chamberlain, Kirill Evdokimov, Jianqing Fan, Christian Hansen, Jerry Hausman, Jean Jacod, Ilze Kalnina, Jia Li, Yingying Li, Oliver Linton, Nour Meddahi, Per Mykland, Ulrich Müller, Andrew Patton, Eric Renault, Jeffrey Russell, Neil Shephard, George Tauchen, Viktor Todorov, Ruey Tsay, and Xinghua Zheng, as well as seminar and conference participants at Brown University, CEMFI, Duke University, Harvard University, MIT, Northwestern University, Peking University, Princeton University, Singapore Management University, University of Amsterdam, University of Chicago, University of Illinois at Chicago, University of Tokyo, the 2015 North American Winter Meeting of the Econometric Society, the CEME Young Econometricians Workshop at Cornell, the NBER-NSF Time Series Conference in Vienna, the 10th International Symposium on Econometric Theory and Applications, the 7th Annual SoFiE Conference, the 2015 Financial Econometrics Conference in Toulouse and the 6th French Econometrics Conference. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.