Principal Component Analysis based on Correlation Matrix with Asynchronous and Noisy High Frequency Data

This paper developed the feasible estimation methodology for the principal component analysis (PCA) based on correlation matrix, which is robust to the noisy and asynchronous high frequency data. The general framework of our methodology is constructed based on the estimation of realized spectral functions with respect to the spot correlation matrix. A new asymptotic representation for the element-wise estimation error of the spot correlation matrix estimate has been derived, resulting in a new bias correction term which is much more complex than that of the PCA based covariance matrix. Central limit theorem and rate of convergence have been developed for the bias-corrected estimator. The standard error estimator has also been proposed. As the empirical study of our methodology, we have constructed the first eigen-portfolio based on the eigenvector estimate corresponding to the largest eigenvalue in the spot correlation matrix. We regress the returns of first eigen-portfolio against that of the market ETF, which obtained non-significant alpha estimate and significant beta estimate which is very close to one