High Frequency Factor Analysis with Partially Observable Factors

This paper considers a novel factor structure -- Partially Observable Factor Model -- where both observable factors and latent factors exist in the model simultaneously. Such factor structure can make sure both interpretability and goodness-of-fit at the same time. Necessary estimation methodologies for this partially observable factor model are developed in this paper for the high frequency data. The proposed estimation methodology is robust to jumps, microstructure noise and asynchronous observation times simultaneously. In the case of finite dimensionality, we provide the estimation theory for the integrated eigenvalues of the residual covariance matrix, which including the bias-corrected estimator, central limit theorem and asymptotic variance estimator. As a result, the asymptotic normality of the bias-corrected estimator can be applied to test the existence of the latent factors. In the case of high dimensionality, we proposed the estimation method for the high dimensional covariance and precision matrices. In contrast to the existing literature, which assuming the residual covariance matrix generated from regression to be weakly correlated or sparse, this paper relaxed such assumptions and designed a new estimator for this task. The theoretical development of this new estimator is non-trivial and the convergence rates are established accordingly. Monte Carlo simulation demonstrates the validity of our estimation methodologies. Empirical study demonstrates that the latent factors significantly exist in the residual process of the high frequency regression