High-Dimensional GARCH Model with L1 Regularization

• Activity Number: 360 - Contributed Poster Presentations: Section on Risk Analysis
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Risk Analysis
• Author(s): Sijie Yao* and Haipeng Xing and Hui Zou
• Companies: and SUNY Stony Brook and University of Minnesota
• Keywords: GARCH; BEKK; L1-penalty; Information arrival; Covariance matrices; Spillover effect

Abstract

The complexity of multivariate GARCH models increases dramatically when the number of the series increases. To address this issue, we propose a general regularization framework for high-dimensional GARCH models, and obtain a penalized quasi-maximum likelihood (PQML) estimator. In the first half of this paper, we give the details of model setting for regularized high-dimensional GARCH and show the sparsity and consistency of the PQML estimator under certain assumptions on L1 penalty function for BEKK(1,1) GARCH model. In the remain part of paper, our theoretical results are confirmed under different settings of simulation study and finally, we apply our method in the real market and give some empirical analysis from our estimation.