A simulation-based comparative study of Bayesian VAR forecasting accuracy under heteroscedasticity

Abstract

This study evaluates the robustness of Bayesian Vector Autoregression (BVAR) models under heteroscedasticity, with the objective of identifying the most reliable approach for forecasting macroeconomic and financial variables in volatile environments. Four BVAR variants were examined: Minnesota prior (BVAR1), Normal-Wishart prior (BVAR2), Stochastic Search Variable Selection (BVAR3), and Hierarchical Shrinkage with SSVS (BVAR4). A Monte Carlo simulation was designed using data generated from VAR processes with heteroscedastic disturbances modeled through ARCH, GARCH, and time-varying covariance structures. Forecast accuracy was assessed using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) across varying levels of variance (low, medium, and large) and sample sizes. Results show that BVAR4 consistently achieved superior accuracy under low and medium heteroscedasticity, particularly with larger samples. Under extreme heteroscedasticity, forecast precision declined for all models, with BVAR3 occasionally rivaling BVAR4. The findings suggest that shrinkage-based BVARs with adaptive selection mechanisms are more robust in environments with mild to moderate volatility. For highly turbulent conditions, however, diagnostic testing, variance-stabilizing transformations, and heteroscedasticity-robust estimation are recommended to improve reliability. These results provide evidence-based guidance for policymakers and practitioners seeking dependable tools for forecasting in uncertain economic contexts.