Learning Latent Factors From Diversified Projections and Its Applications to Over-Estimated and Weak Factors

Jianqing Fan and Yuan Liao

Journal of the American Statistical Association, 2022, vol. 117, issue 538, 909-924

Abstract: Estimations and applications of factor models often rely on the crucial condition that the number of latent factors is consistently estimated, which in turn also requires that factors be relatively strong, data are stationary and weakly serially dependent, and the sample size be fairly large, although in practical applications, one or several of these conditions may fail. In these cases, it is difficult to analyze the eigenvectors of the data matrix. To address this issue, we propose simple estimators of the latent factors using cross-sectional projections of the panel data, by weighted averages with predetermined weights. These weights are chosen to diversify away the idiosyncratic components, resulting in “diversified factors.” Because the projections are conducted cross-sectionally, they are robust to serial conditions, easy to analyze and work even for finite length of time series. We formally prove that this procedure is robust to over-estimating the number of factors, and illustrate it in several applications, including post-selection inference, big data forecasts, large covariance estimation, and factor specification tests. We also recommend several choices for the diversified weights. Supplementary materials for this article are available online.

Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2020.1831927 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:117:y:2022:i:538:p:909-924

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2020.1831927

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().