<i>L</i><sub>1</sub> Regularization for High-Dimensional Multivariate GARCH Models
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 likel...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Risks |
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| Online Access: | https://www.mdpi.com/2227-9091/12/2/34 |
| _version_ | 1797297108336771072 |
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| author | Sijie Yao Hui Zou Haipeng Xing |
| author_facet | Sijie Yao Hui Zou Haipeng Xing |
| author_sort | Sijie Yao |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-07T22:15:30Z |
| format | Article |
| id | doaj.art-fb051981c390414bb930e09f9f86e751 |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-03-07T22:15:30Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-fb051981c390414bb930e09f9f86e7512024-02-23T15:33:20ZengMDPI AGRisks2227-90912024-02-011223410.3390/risks12020034<i>L</i><sub>1</sub> Regularization for High-Dimensional Multivariate GARCH ModelsSijie Yao0Hui Zou1Haipeng Xing2Department of Biostatistics and Bioinformatics, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL 33612, USASchool of Statistics, University of Minnesota, Minneapolis, MN 55455, USADepartment of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11733, USAThe 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.https://www.mdpi.com/2227-9091/12/2/34Markov chain Monte Carlomultivariate GARCHspilloverstochastic approximation |
| spellingShingle | Sijie Yao Hui Zou Haipeng Xing <i>L</i><sub>1</sub> Regularization for High-Dimensional Multivariate GARCH Models Risks Markov chain Monte Carlo multivariate GARCH spillover stochastic approximation |
| title | <i>L</i><sub>1</sub> Regularization for High-Dimensional Multivariate GARCH Models |
| title_full | <i>L</i><sub>1</sub> Regularization for High-Dimensional Multivariate GARCH Models |
| title_fullStr | <i>L</i><sub>1</sub> Regularization for High-Dimensional Multivariate GARCH Models |
| title_full_unstemmed | <i>L</i><sub>1</sub> Regularization for High-Dimensional Multivariate GARCH Models |
| title_short | <i>L</i><sub>1</sub> Regularization for High-Dimensional Multivariate GARCH Models |
| title_sort | i l i sub 1 sub regularization for high dimensional multivariate garch models |
| topic | Markov chain Monte Carlo multivariate GARCH spillover stochastic approximation |
| url | https://www.mdpi.com/2227-9091/12/2/34 |
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