Quasi Maximum Likelihood Analysis of High Dimensional Constrained Factor Models

57 Pages Posted: 24 Jan 2019 Last revised: 18 Mar 2022

See all articles by Kunpeng Li

Kunpeng Li

Capital University of Economics and Business

Qi Li

Texas A&M University

Lina Lu

Federal Reserve Banks - Federal Reserve Bank of Boston

Date Written: April, 2018

Abstract

Factor models have been widely used in practice. However, an undesirable feature of a high dimensional factor model is that the model has too many parameters. An effective way to address this issue, proposed in a seminal work by Tsai and Tsay (2010), is to decompose the loadings matrix by a high-dimensional known matrix multiplying with a low-dimensional unknown matrix, which Tsai and Tsay (2010) name the constrained factor models. This paper investigates the estimation and inferential theory of constrained factor models under large-N and large-T setup, where N denotes the number of cross sectional units and T the time periods. We propose using the quasi maximum likelihood method to estimate the model and investigate the asymptotic properties of the quasi maximum likelihood estimators, including consistency, rates of convergence and limiting distributions. A new statistic is proposed for testing the null hypothesis of constrained factor models against the alternative of standard factor models. Partially constrained factor models are also investigated. Monte carlo simulations confirm our theoretical results and show that the quasi maximum likelihood estimators and the proposed new statistic perform well in finite samples. We also consider the extension to an approximate constrained factor model where the idiosyncratic errors are allowed to be weakly dependent processes.

Keywords: Constrained factor models, Maximum likelihood estimation, High dimensionality, Inferential theory

JEL Classification: C13, C38

Suggested Citation

Li, Kunpeng and Li, Qi and Lu, Lina, Quasi Maximum Likelihood Analysis of High Dimensional Constrained Factor Models (April, 2018). FRB Boston Risk and Policy Analysis Unit Paper No. RPA 18-2, Available at SSRN: https://ssrn.com/abstract=3321602

Kunpeng Li

Capital University of Economics and Business ( email )

Zhangjialukou 121, Huaxiang
Fengtai district
Beijing, 100070
China

Qi Li (Contact Author)

Texas A&M University ( email )

7101 University Avenue
STEM 318 H
Texarkana, TX 75503
United States

Lina Lu

Federal Reserve Banks - Federal Reserve Bank of Boston ( email )

600 Atlantic Avenue
Boston, MA 02210
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
35
Abstract Views
528
PlumX Metrics