High frequency principal component analysis based on correlation matrix that is robust to jumps, microstructure noise and asynchronous observation times

This paper developed the high frequency estimation for the principal component analysis (PCA) based on correlation matrix. This estimation methodology is robust to jumps, microstructure noise and asynchronous observation times simultaneously, which is enabled by the newly proposed Truncated and Smoothed Two-Scales Realized Volatility (Truncated S-TSRV) estimator. 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.