A time-varying latent factor model with GARCH noise for high-dimensional covariance matrix estimation

Yuwen Ruan; Xingfa Zhang; Yujiao Liu; Yan Wang; Tianli Lei; Yuwen Ruan; Xingfa Zhang; Yujiao Liu; Yan Wang; Tianli Lei

doi:10.3934/math.2026230

AIMS Mathematics

2026, Volume 11, Issue 3: 5575-5599. doi: 10.3934/math.2026230

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Research article

A time-varying latent factor model with GARCH noise for high-dimensional covariance matrix estimation

1.
School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China
2.
Business School, Asia Pacific University of Technology and Innovation, Kuala Lumpur 57000, Malaysia
3.
Institute of Applied Mathematics, Shenzhen Polytechnic University, Shenzhen 518051, China

Received: 27 December 2025 Revised: 12 February 2026 Accepted: 26 February 2026 Published: 05 March 2026
MSC : 62F12, 62G05, 62M10

In this paper, we established a time-varying latent factor model with GARCH (generalized autoregressive conditional heteroskedasticity) noise to study volatilities (conditional covariance matrix) under the high-dimensional framework, when factors are unobservable, factor loadings are time-varying, and the idiosyncratic error term shows heteroskedasticity. A projection method was proposed for more-precise estimation of the conditional covariance matrix. We demonstrated that our model is robust when the dimensionality and sample size are large. Asymptotic theories were developed for the proposed estimation. A simulation study was conducted to evaluate the performance of the proposed model, and a real example was provided to illustrate this approach.
- time-varying factor model,
- multivariate GARCH,
- high-dimensionality,
- conditional covariance matrix
Citation: Yuwen Ruan, Xingfa Zhang, Yujiao Liu, Yan Wang, Tianli Lei. A time-varying latent factor model with GARCH noise for high-dimensional covariance matrix estimation[J]. AIMS Mathematics, 2026, 11(3): 5575-5599. doi: 10.3934/math.2026230

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Abstract

In this paper, we established a time-varying latent factor model with GARCH (generalized autoregressive conditional heteroskedasticity) noise to study volatilities (conditional covariance matrix) under the high-dimensional framework, when factors are unobservable, factor loadings are time-varying, and the idiosyncratic error term shows heteroskedasticity. A projection method was proposed for more-precise estimation of the conditional covariance matrix. We demonstrated that our model is robust when the dimensionality and sample size are large. Asymptotic theories were developed for the proposed estimation. A simulation study was conducted to evaluate the performance of the proposed model, and a real example was provided to illustrate this approach.

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