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

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.

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Informasi Detail

Judul Seri

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (JASA); Vol.117 No.538 June 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 909-924

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

PRINCIPAL COMPONENTS
LARGE DIMENSIONS
RANDOM PROJECTIONS
FACTOR-AUGMENTED REGRESSION
OVER-ESTIMATING THE NUMBER OF FACTORS

Info Detail Spesifik

https://doi.org/10.1080/01621459.2020.1831927

Pernyataan Tanggungjawab

Jianqing Fan, Yuan Liao

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