Regularizing Bayesian predictive regressions

Regularizing Bayesian predictive regressions provides a framework for prior sensitivity analysis via the regularization path. We jointly regularize both expectations and covariance matrices using a pair of shrinkage priors. Our methodology applies directly to vector autoregressions and seemingly unrelated regressions (SUR). By exploiting a duality between penalties and priors, we reinterpret two classic macrofinance studies: equity premium predictability and macroforecastability of bond risk premia. We find those plausible prior specifications for predictability for excess S&P 500 returns exist, using predictors as book-to-market ratios, consumption–wealth 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 are sensitive to prior specifications. Finally, we conclude with directions for future research.