Eigenvalue tests for the number of latent factors in short panels
Additional information
Authors
Fortin A. P.,
Gagliardini P.,
Scaillet O.
Type
Journal Article
Year
2023
Language
English
Abstract
This article studies new tests for the number of latent factors in a large cross-sectional factor model with small time dimension. These tests are based on the eigenvalues of variance–covariance matrices of (possibly weighted) asset returns and rely on either an assumption of spherical errors, or instrumental variables for factor betas. We establish the asymptotic distributional results using expansion theorems based on perturbation theory for symmetric matrices. Our framework accommodates semi-strong factors in the systematic components. We propose a novel statistical test for weak factors against strong or semi-strong factors. We provide an empirical application to U.S. equity data. Evidence for a different number of latent factors according to market downturns and market upturns is statistically ambiguous in the considered subperiods. In particular, our results contradict the common wisdom of a single-factor model in bear markets.
Keywords
Factor model, Principal component analysis, Panel data, Large n and fixed T asymptotics, Equity returns
Journal
Journal of financial econometrics
Volume
00
Pages (or article number)
nbad024
Diffusion
License
CC BY
Visibility
Public
Status open access
Hybrid
