Estimation of common factors for microstructure noise and efficient price in a high-frequency dual factor model

We develop the Double Principal Component Analysis (DPCA) based on a dual factor structure for high-frequency intraday returns contaminated with microstructure noise. The allows noise in addition to efficient log-prices. construct estimators of factors both log-prices and as well their common components, provide uniform consistency these when number assets sampling frequency go infinity. In Monte Carlo exercise, we compare our DPCA method PCA-VECM method. Finally, an empirical analysis S&P 500 Index constituents provides evidence co-movement that distinguishes from latent systematic risk factors.