Model Selection for Vector Autoregressive Processes via Adaptive Lasso

Abstract

Determination of the best subset is an important step in vector autoregressive (VAR) modeling. Traditional methods either conduct subset selection and parameter estimation separately or compute expensively. In this article, we propose a VAR model selection procedure using adaptive Lasso, for it is computational efficient and can select subset and estimate parameters simultaneously. By proper choice of tuning parameters, we can choose the correct subset and obtain the asymptotic normality of the non zero parameters. Simulation studies and real data analysis show that adaptive Lasso performs better than existing methods in VAR model fitting and prediction.

Keywords:

• Adaptive lasso
• Bayesian information criterion
• Least angle regression algorithm
• Oracle property
• Order selection
• Subset selection
• Vector autoregressive models

Mathematics Subject Classification:

• Primary 62M10
• Secondary 91B84

Acknowledgments

The authors sincerely thank Professor Nan-Jung Hsu (Institute of Statistics, National Tsing-Hua University, Taiwan, China) for his valuable suggestion which improve our manuscript. The author's research is supported partly by NSFC Grant 11071045 and Shanghai Leading Academic Discipline Project, Project Number: B210.