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

28 Pages Posted: 1 Nov 2016

See all articles by Xinbing Kong

Xinbing Kong

Soochow University

Zhi Liu

University of Macau

Zhou Wang

National University of Singapore (NUS)

Date Written: May 1, 2016

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.

Keywords: Continuous time factor model, High dimensional Ito process, Driving process

JEL Classification: C13, C14, C55, C58

Suggested Citation

Kong, Xinbing and Liu, Zhi and Wang, Zhou, A Central Limit Theorem for the Number of Factors with High Frequency Data (May 1, 2016). Available at SSRN: https://ssrn.com/abstract=2862277 or http://dx.doi.org/10.2139/ssrn.2862277

Xinbing Kong (Contact Author)

Soochow University ( email )

No. 1 Shizi Street
Taipei, Jiangsu 215006
Taiwan

Zhi Liu

University of Macau ( email )

P.O. Box 3001
Macau

Zhou Wang

National University of Singapore (NUS)

1E Kent Ridge Road
NUHS Tower Block Level 7
Singapore, 119228
Singapore

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