Regularizing Bayesian predictive regressions provides a framework for prior sensitivity analysis via the regularization path. We jointly regularize both expectations and variance-covariance matrices using a pair of shrinkage priors. Our methodology applies directly to vector autoregressions (VAR) and seemingly unrelated regressions (SUR). By exploiting a duality between penalties and priors, we reinterpret two classic macro-finance studies: equity premium predictability and macro forecastability of bond risk premia. We find that there exist plausible prior specifications for predictability for excess S&P 500 returns using predictors book-to-market ratios, CAY (consumption, wealth, income ratio), and T-bill rates. We evaluate our forecasts using a market-timing strategy and show how ours outperforms buy-and-hold. We also predict multiple bond excess returns involving a high-dimensional set of macroeconomic fundamentals with a regularized SUR model. We find the predictions from latent factor models such as PCA to be sensitive to prior specifications. Finally, we conclude with directions for future research.

中文翻译：

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正则化贝叶斯预测回归

正则化贝叶斯预测回归为通过正则化路径进行事前敏感性分析提供了框架。我们使用一对收缩先验对期望矩阵和方差-协方差矩阵进行联合正则化。我们的方法直接适用于向量自回归（VAR）和看似无关的回归（SUR）。通过利用罚金和先验之间的对偶关系，我们重新解释了两个经典的宏观金融研究：股票溢价可预测性和债券风险溢价的宏观可预测性。我们发现，使用预测指标的市销率，CAY（消费，财富，收入比率）和国库券利率，对于标准普尔500指数超额收益的可预测性存在合理的先验规范。我们使用市场时机策略评估我们的预测，并显示我们的表现如何优于买入和持有。我们还使用正则化SUR模型预测涉及高维宏观经济基本面的多重债券超额收益。我们发现来自潜在因素模型（例如PCA）的预测对先前的规范敏感。最后，我们总结了未来研究的方向。