High frequency factor analysis with partially observable factors

Abstract

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.

When the observable factors are exogenous, 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.

When the observable factors are endogenous, we propose a novel framework of high frequency unsupervised exogenous component learning (HF-UECL), which can help people quantify the contributions of the observable factors into the latent factors. This is the first work on high frequency instrumental variables, and it can be regard as a necessary and non-trivial extension of the Projected-PCA in the world of continuous-time model. Statistical inferences have been established for the loadings of the observable factors onto the latent factors.

Monte Carlo simulation demonstrates the validity of our estimation methodologies. Empirical study demonstrates that (i) in the exogenous setting, the latent factors significantly exist in the residual process of the high frequency regression; (ii) in the endogenous setting, the correlations between the observable factors and latent factors do exist significantly.