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<p>In this paper, we establish a semi-parametric factor-GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model to estimate covariance matrix within a high-dimensional framework where both factors and factor loadings are unobservable and the data shows heteroskedasticity. The basic idea is to use projection technique to remove noise components, leading to a more precise estimation of the covariance matrix. We demonstrate that our model is robust when the sample size is finite and is particularly effective in high-dimensionality, low-sample-size settings. Asymptotic theories are developed for the proposed estimation. A simulation study is conducted to evaluate the performance of the proposed model, and a real example is provided to illustrate this approach.</p>

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A semi-parametric factor-GARCH model for high dimensional covariance matrix estimation

  • 期刊论文

  • 发表日期：

    2025年5月26日

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  • Yuwen Ruan,
  • Xingfa Zhang,
  • Yujiao Liu

摘要

In this paper, we establish a semi-parametric factor-GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model to estimate covariance matrix within a high-dimensional framework where both factors and factor loadings are unobservable and the data shows heteroskedasticity. The basic idea is to use projection technique to remove noise components, leading to a more precise estimation of the covariance matrix. We demonstrate that our model is robust when the sample size is finite and is particularly effective in high-dimensionality, low-sample-size settings. Asymptotic theories are developed for the proposed estimation. A simulation study is conducted to evaluate the performance of the proposed model, and a real example is provided to illustrate this approach.