STRONG SELECTION CONSISTENCY OF BAYESIAN VECTOR AUTOREGRESSIVE MODELS BASED ON A PSEUDO-LIKELIHOOD APPROACH

• 成果类型: Article
• 署名作者: Ghosh, Satyajit; Khare, Kshitij; Michailidis, George
• 署名单位: Rutgers University System; Rutgers University New Brunswick; State University System of Florida; University of Florida; State University System of Florida; University of Florida
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS1992
• 发表日期: 2021
• 页码: 1267-1299
• 关键词: VARIABLE SELECTION

摘要

Vector autoregressive (VAR) models aim to capture linear temporal interdependencies among multiple time series. They have been widely used in macroeconomics and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which will provide novel insights into the role of temporal dependence for regularized estimates of the models parameters. However, hardly anything is known regarding posterior model selection consistency for Bayesian VAR models in such regimes. In this work, we develop a pseudo-likelihood based Bayesian approach for consistent variable selection in high-dimensional VAR models by considering hierarchical normal priors on the autoregressive coefficients, as well as on the model space. We establish strong selection consistency of the proposed method, namely that the posterior probability assigned to the true underlying VAR model converges to one under high-dimensional scaling where the dimension p of the VAR system grows nearly exponentially with the sample size n. Further, the result is established under mild regularity conditions on the problem parameters. Finally, as a by-product of these results, we also establish strong selection consistency for the sparse high-dimensional linear regression model with serially correlated regressors and errors.