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A Factor-GARCH Model for High Dimensional Volatilities

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Abstract

This paper proposes a method for modelling volatilities (conditional covariance matrices) of high dimensional dynamic data. We combine the ideas of approximate factor models for dimension reduction and multivariate GARCH models to establish a model to describe the dynamics of high dimensional volatilities. Sparsity condition and thresholding technique are applied to the estimation of the error covariance matrices, and quasi maximum likelihood estimation (QMLE) method is used to estimate the parameters of the common factor conditional covariance matrix. Asymptotic theories are developed for the proposed estimation. Monte Carlo simulation studies and real data examples are presented to support the methodology.

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Authors and Affiliations

  1. School of Economics and Statistics, Guangzhou Unversity, Guangzhou, 510006, China

    Xiao-ling Li, Yuan Li & Xing-fa Zhang

  2. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China

    Xiao-ling Li

  3. Department of Mathematics & Statistics, University of Strathclyde, Glasgow, G1 1XH, UK

    Jia-zhu Pan

Authors
  1. Xiao-ling Li
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  2. Yuan Li
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  3. Jia-zhu Pan
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  4. Xing-fa Zhang
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Corresponding author

Correspondence to Xing-fa Zhang.

Additional information

This paper is supported by the National Natural Science Foundation of China (Nos. 11731015, 11701116), Innovative Team Project of Ordinary Universities in Guangdong Province (No. 2020WCXTD018) and Guangzhou University Research Fund (Nos. YG2020029, YH202108).

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Li, Xl., Li, Y., Pan, Jz. et al. A Factor-GARCH Model for High Dimensional Volatilities. Acta Math. Appl. Sin. Engl. Ser. 38, 635–663 (2022). https://doi.org/10.1007/s10255-022-1104-6

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  • DOI: https://doi.org/10.1007/s10255-022-1104-6

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