Combining shrinkage and sparsity in conjugate vector autoregressive models.

Area of Science:

• Econometrics
• Statistical Modeling
• Bayesian Inference

Background:

• Conjugate priors enable fast inference in large-dimensional vector autoregressive (VAR) models.
• A key limitation of conjugate priors is the requirement for identical explanatory variables across all equations.
• This restricts the flexibility and applicability of Bayesian VAR models in complex scenarios.

Purpose of the Study:

• To propose a postprocessing technique for conjugate Bayesian VAR models.
• To enable effective equation-specific covariate selection.
• To overcome the limitation of identical covariate sets across equations.

Main Methods:

• The proposed method postprocesses posterior estimates from a conjugate Bayesian VAR.
• It combines shrinkage and sparsity in both VAR coefficients and error variance-covariance matrices.
• This approach enhances computational tractability for high-dimensional models.

Main Results:

• The method effectively performs equation-specific covariate selection.
• It significantly reduces estimation uncertainty in large dimensions.
• The approach maintains computational efficiency compared to existing methods.

Conclusions:

• The proposed postprocessing technique offers a practical solution for covariate selection in large-dimensional Bayesian VAR models.
• It enhances model flexibility by allowing equation-specific variable inclusion.
• The method demonstrates utility in both synthetic data analysis and real-world forecasting applications.