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L 1 Regularization for High-Dimensional Multivariate GARCH Models

Author

Listed:
  • Sijie Yao

    (Department of Biostatistics and Bioinformatics, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL 33612, USA)

  • Hui Zou

    (School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA)

  • Haipeng Xing

    (Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11733, USA)

Abstract

The complexity of estimating multivariate GARCH models increases significantly with the increase in the number of asset series. To address this issue, we propose a general regularization framework for high-dimensional GARCH models with BEKK representations, and obtain a penalized quasi-maximum likelihood (PQML) estimator. Under some regularity conditions, we establish some theoretical properties, such as the sparsity and the consistency, of the PQML estimator for the BEKK representations. We then carry out simulation studies to show the performance of the proposed inference framework and the procedure for selecting tuning parameters. In addition, we apply the proposed framework to analyze volatility spillover and portfolio optimization problems, using daily prices of 18 U.S. stocks from January 2016 to January 2018, and show that the proposed framework outperforms some benchmark models.

Suggested Citation

  • Sijie Yao & Hui Zou & Haipeng Xing, 2024. "L 1 Regularization for High-Dimensional Multivariate GARCH Models," Risks, MDPI, vol. 12(2), pages 1-28, February.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:2:p:34-:d:1333357
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    References listed on IDEAS

    as
    1. Weide, R. van der, 2002. "Generalized Orthogonal GARCH. A Multivariate GARCH model," CeNDEF Working Papers 02-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    2. Hafner, Christian M. & Herwartz, Helmut & Maxand, Simone, 2022. "Identification of structural multivariate GARCH models," Journal of Econometrics, Elsevier, vol. 227(1), pages 212-227.
    3. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
    4. Michael McAleer & Suhejla Hoti & Felix Chan, 2009. "Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 422-440.
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