TY - JOUR
T1 - L1 Regularization for High-Dimensional Multivariate GARCH Models
AU - Yao, Sijie
AU - Zou, Hui
AU - Xing, Haipeng
N1 - Publisher Copyright:
© 2024 by the authors.
PY - 2024/2
Y1 - 2024/2
N2 - 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.
AB - 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.
KW - Markov chain Monte Carlo
KW - multivariate GARCH
KW - spillover
KW - stochastic approximation
UR - http://www.scopus.com/inward/record.url?scp=85187268448&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85187268448&partnerID=8YFLogxK
U2 - 10.3390/risks12020034
DO - 10.3390/risks12020034
M3 - Article
AN - SCOPUS:85187268448
SN - 2227-9091
VL - 12
JO - Risks
JF - Risks
IS - 2
M1 - 34
ER -