Vector autoregression (VAR) models are widely used for forecasting and macroeconomic analysis, yet they remain limited by their reliance on a linear parameterization. Recent research has introduced nonparametric alternatives, such as Bayesian additive regression trees (BART), which provide flexibility without strong parametric assumptions. However, existing BART-based frameworks do not account for time dependency or allow for sparse estimation in the construction of regression tree priors, leading to noisy and inefficient high-dimensional representations. This paper introduces a sparsity-inducing Dirichlet hyperprior on the regression tree's splitting probabilities, allowing for automatic variable selection and high-dimensional VARs. Additionally, we propose a structured shrinkage prior that decreases the probability of splitting on higher-order lags, aligning with the Minnesota prior's principles. Empirical results demonstrate that our approach improves predictive accuracy over the baseline BART prior and Bayesian VAR (BVAR), particularly in capturing time-dependent relationships and enhancing density forecasts. These findings highlight the potential of developing domain-specific nonparametric methods in macroeconomic forecasting.

翻译：向量自回归（VAR）模型被广泛应用于预测和宏观经济分析，但其仍受限于对线性参数化的依赖。近期研究引入了非参数替代方法，如贝叶斯加性回归树（BART），该方法无需强参数假设即可提供灵活性。然而，现有的基于BART的框架未考虑时间依赖性，也未在回归树先验的构建中允许稀疏估计，导致高维表示存在噪声且效率低下。本文在回归树的分割概率上引入了一种诱导稀疏性的狄利克雷超先验，从而实现了自动变量选择和高维VAR建模。此外，我们提出了一种结构化收缩先验，该先验降低了基于高阶滞后项进行分割的概率，符合明尼苏达先验的原则。实证结果表明，相较于基线BART先验和贝叶斯VAR（BVAR），我们的方法在预测准确性方面有所提升，特别是在捕捉时间依赖关系和增强密度预测方面。这些发现凸显了在宏观经济预测中开发领域特异性非参数方法的潜力。