Estimation of Weak Factor Models

ISER DP No. 1053

46 Pages Posted: 17 May 2019 Last revised: 22 Sep 2020

See all articles by Yoshimasa Uematsu

Yoshimasa Uematsu

Tohoku University - Graduate School of Economics & Management

Takashi Yamagata

University of York - Department of Economics and Related Studies; Osaka University - Institute of Social and Economic Research

Date Written: September 22, 2020

Abstract

This paper investigates estimation of sparsity-induced weak factor (sWF) models, with large cross-sectional and time-series dimensions (N and T, respectively). It assumes that the kth largest eigenvalue of data covariance matrix grows proportionally to N^ak with unknown exponents 0 < ak <= 1 for k=1,...,r. Employing the same rotation of the principal component (PC) estimator, in the sWF models the growth rate ak is linked to the degree of sparsity of kth factor loadings. This is much weaker than the typical assumption on the recent factor models, in which all the r largest eigenvalues diverge proportionally to N. We apply the SOFAR method of Uematsu et al. (2019) to estimate the sWF models and derive the estimation error bound. Importantly, our method yields consistent estimation of ak's as well. A finite sample experiment shows that the performance of the new estimator uniformly dominates that of the PC estimator. We apply our method to forecasting bond yields and results demonstrate that our method outperforms that based on the PC. In another application we analyze S&P500 firm security returns and find that the first factor is consistently near strong while the others are indeed weak.

Keywords: Sparsity-induced weak factor models, (Adaptive) SOFAR estimator, Estimation error bound, Estimating diverging exponents, Interpreting factors, Group factor structure.

JEL Classification: C13, C23, C38, C58

Suggested Citation

Uematsu, Yoshimasa and Yamagata, Takashi, Estimation of Weak Factor Models (September 22, 2020). ISER DP No. 1053, Available at SSRN: https://ssrn.com/abstract=3374750 or http://dx.doi.org/10.2139/ssrn.3374750

Yoshimasa Uematsu

Tohoku University - Graduate School of Economics & Management ( email )

Kawauchi, Aoba-ku
Sendai, 980-8576
Japan

Takashi Yamagata (Contact Author)

University of York - Department of Economics and Related Studies ( email )

Heslington
York, YO1 5DD
United Kingdom

Osaka University - Institute of Social and Economic Research ( email )

6-1, Mihogaoka
Suita, Osaka 567-0047
Japan

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