High-Dimensional Vector Autoregression (VAR)

• Activity Number: 73
• Type: Topic Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Sumanta Basu*+
• Companies: University of Michigan
• Keywords: vector autoregression ; time series ; variable selection ; graphical model ; network

Abstract

We consider the problem of estimation and model selection in high dimenisonal vector autorgressive (VAR) processes. High dimensional VAR models are popular in the analyses of Economic and Financial data, where one is typically interested in learning the nature of relationship among a large number of variables from time series data. We propose an l1-regualized regression framework for estimaing the model coefficients. Assuming the order of the VAR process is known, we establish estimation and model selection consistency of our estimates leading to improved prediction accuracy over standard least square estimates. We demonstrate the performance of the proposed methodology using an extensive set of simulation studies and a real data application from financial econometrics.