L1 Regularization for High-Dimensional Multivariate GARCH Models

Sijie Yao, Hui Zou, Haipeng Xing

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number34
Issue number2
StatePublished - Feb 2024

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© 2024 by the authors.


  • Markov chain Monte Carlo
  • multivariate GARCH
  • spillover
  • stochastic approximation


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