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Volume 14
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Article

High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model

by
Xiaoling Li
1,2,
Xingfa Zhang
1,* and
Yuan Li
1
1
School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China
2
College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China
*
Author to whom correspondence should be addressed.
Symmetry 2022, 14(1), 158; https://doi.org/10.3390/sym14010158
Submission received: 11 November 2021 / Revised: 20 December 2021 / Accepted: 9 January 2022 / Published: 13 January 2022
(This article belongs to the Section B: Mathematics)
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Abstract

Estimation of a conditional covariance matrix is an interesting and important research topic in statistics and econometrics. However, modelling ultra-high dimensional dynamic (conditional) covariance structures is known to suffer from the curse of dimensionality or the problem of singularity. To partially solve this problem, this paper establishes a model by combining the ideas of a factor model and a symmetric GARCH model to describe the dynamics of a high-dimensional conditional covariance matrix. Quasi maximum likelihood estimation (QMLE) and least square estimation (LSE) methods are used to estimate the parameters in the model, and the plug-in method is introduced to obtain the estimation of conditional covariance matrix. Asymptotic properties are established for the proposed method, and simulation studies are given to demonstrate its performance. A financial application is presented to support the methodology.
Keywords: factor model; high-dimensional conditional covariance matrix; GARCH model factor model; high-dimensional conditional covariance matrix; GARCH model

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MDPI and ACS Style

Li, X.; Zhang, X.; Li, Y. High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model. Symmetry 2022, 14, 158. https://doi.org/10.3390/sym14010158

AMA Style

Li X, Zhang X, Li Y. High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model. Symmetry. 2022; 14(1):158. https://doi.org/10.3390/sym14010158

Chicago/Turabian Style

Li, Xiaoling, Xingfa Zhang, and Yuan Li. 2022. "High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model" Symmetry 14, no. 1: 158. https://doi.org/10.3390/sym14010158

APA Style

Li, X., Zhang, X., & Li, Y. (2022). High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model. Symmetry, 14(1), 158. https://doi.org/10.3390/sym14010158

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