Statistics Seminar（2018-08）

Topic: The Five Trolls under the Bridge: Principal Component Analysis with Asynchronous and Noisy High Frequency Data

Speaker: Dachuan Chen, University of Illinois at Chicago

Time: Monday, June 11, 14:00-15:00

Place: Room 217, Guanghua Building 2

Abstract:

We develop a principal component analysis (PCA) for high frequency data. As in Northern fairly tales, there are trolls waiting for the explorer. The first three trolls are market microstructure noise, asynchronous sampling times, and edge effects in estimators. To get around these, a robust estimator of spot covariance matrix is developed based on the Smoothed TSRV (Mykland et al. (2017)). The fourth troll is how to pass from estimated time-varying covariance matrix to PCA. Under finite dimensionality, we develop this methodology through the estimation of realized spectral functions. Rates of convergence and central limit theory, as well as an estimator of standard error, are established. The fifth troll is high dimension on top of high frequency, where we also develop PCA. With the help of a new identity concerning the spot principal orthogonal complement, the high-dimensional rates of convergence have been studied by freeing several strong assumptions in classical PCA. As an application, we show that our first principal component (PC) potentially outperforms the S&P 100 market index, while three of the next four PCs are cointegrated with two of the Fama-French non-market factors. (This is the joint work with Per Mykland and Lan Zhang.)

Introduction:

Dachuan Chen is currently a Ph.D. candidate in Business Administration at University of Illinois at Chicago. His dissertation advisors are Professor Lan Zhang (from UIC) and Professor Per Mykland (from University of Chicago). Dachuan received his B.S. degree in Statistics from Nankai University in 2012. He was a Ph.D. student in the Computer Science and Information System Program at University of Colorado at Denver from 2012 to 2014. Dachuan’s research interests include financial econometrics and high frequency econometrics. His research papers have been published in several leading journals, including Journal of Econometrics and IIE Transactions.

Your participation is warmly welcomed!