Strong selection consistency of Bayesian vector autoregressive models based on a pseudo-likelihood approach
基于伪似然的贝叶斯向量自回归模型强选择一致性AI 解读 ↓
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基于伪似然的贝叶斯向量自回归模型强选择一致性
- 研究问题
- 在高维向量自回归中，贝叶斯方法能否使真实模型的后验概率趋于一，并允许系统维度随样本量快速增长？
- 方法与思路
- 作者以伪似然构建贝叶斯变量选择方法，对自回归系数及模型空间设置层次先验，并分析时间依赖下的模型选择一致性。
- 材料陈述的贡献
- 摘要称在系统维度近乎指数增长时建立强选择一致性，并将相关结果扩展到解释变量与误差均存在序列相关的稀疏回归。
- 阅读关注点
- 应核对伪似然构造、先验与真实模型的条件、维度增长限制，以及时间依赖如何影响选择一致性和回归扩展结果。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要；所谓温和条件的具体内容未说明，选择一致性不直接保证冲击识别或有限样本表现。
原文摘要
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.