Regularization for Stationary Multivariate Time Series

• Activity Number: 476
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Yan Sun*+ and Xiaodong Lin
• Companies: University of Cincinnati and Rutgers University
• Keywords: Multivariate ; GARCH ; Penalty ; Sparsity ; Oracle Property

Abstract

The complexity of multivariate time series models grows dramatically when the number of component series increases. In this paper, we develop a regularization framework for multivariate time series models based on the penalized likelihood method. We show that under mild conditions, the regularized estimators are sparse-consistent and possess the well-known oracle property. This framework provides a theoretical foundation for addressing the curse of dimensionality in multivariate econometric models. We illustrate the utility of our method by developing a sparse version of the full-factor multivariate GARCH model. We successfully apply this model to simulated data as well as the daily log return data of the Dow Jones industrial average component stocks.