Estimation of Sparsity-Induced Weak Factor Models

ISER DP No. 1053

67 Pages Posted: 17 May 2019 Last revised: 7 Oct 2021

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: October 6, 2021

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 a data covariance matrix grows proportionally to N^alpha_k with unknown exponents 0 < alpha_k <= 1 for k=1,...,r. Employing the same rotation of the principal components (PC) estimator, the growth rate alpha_k 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 method of sparse orthogonal factor regression (SOFAR) by Uematsu et al (2018) to estimate the sWF models and derive the estimation error bound. Importantly, our method also yields consistent estimation of alpha_k. 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 the results demonstrate that our method outperforms that based on the PC. We also analyze S&P500 firm security returns and find that the first factor is consistently near strong while the others are 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 Sparsity-Induced Weak Factor Models (October 6, 2021). 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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