Lag-Adaptive Hierarchical Sparse Bayesian Panel VAR Modeling for High-Dimensional Time Series Systems

Abstract High-dimensional panel vector autoregressive (PVAR) models have become increasingly important for analyzing complex dynamic interactions in multivariate time series systems. However, conventional estimation methods often suffer from overparameterization, multicollinearity, and poor forecasting performance, particularly when the number of parameters grows rapidly relative to the sample size. To address these challenges, this study proposes a Lag-Adaptive Hierarchical Sparse Bayesian Panel Vector Autoregressive (LAHS-BPVAR) model that integrates adaptive lag regularization, hierarchical global-local shrinkage, and sparse Bayesian learning within a unified framework. The proposed model introduces a novel prior covariance structure in which coefficient variances decay according to a hybrid lag-adaptive mechanism combining polynomial and exponential shrinkage, allowing automatic penalization of distant lags while preserving relevant short-run dynamics. A hierarchical sparse prior based on global-local shrinkage further enables adaptive variable selection in high-dimensional settings. Theoretical analysis establishes posterior contraction and sparse support recovery consistency under standard regularity conditions, providing formal asymptotic justification for the proposed estimator. Estimation is performed using a Gibbs sampler with Metropolis-Hastings updates for non-conjugate hyperparameters. Monte Carlo simulation results demonstrate competitive estimation and forecasting performance relative to conventional VAR, Minnesota Bayesian VAR, LASSO VAR, and standard Horseshoe Bayesian VAR. The proposed framework consistently achieves improved sparse support recovery through more effective control of false positive coefficient selection while maintaining estimation accuracy. An empirical application to Indonesian macroeconomic time series further demonstrates the practical effectiveness of the proposed framework in capturing dynamic economic relationships while maintaining model parsimony. The findings suggest that the proposed methodology provides a robust and flexible solution for high-dimensional panel time series modeling.