A Central Limit Theorem for the Number of Factors with High Frequency Data

Abstract

In the literature, consistency of the estimates of the number of factors for both the discrete and continuous time factor models has been extensively studied recently. But the central limit theorem has long been unsolved. In this paper, alternative to the PCA-based approach, we construct a new estimator of the number of common factors of the continuous time factor model using large panel high-frequency data contaminated with noise. We establish the central limit theorem of the new estimator and then apply it to the statistical inference on the number of common factors. Compared with the PCA-based estimators in the existing literatures, ours is proved to have asymptotic normal distribution and robust to the presence of the microstructure noise.