Regularizing Bayesian Predictive Regressions
35 Pages Posted: 17 Aug 2016 Last revised: 25 Oct 2021
Date Written: June 6, 2016
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.
Keywords: Bayesian predictive regression; prior sensitivity analysis; maximum-a-posteriori; equity-premium predictability; bond risk premia; predictor selection.
JEL Classification: C11, C55, G11, G12
Suggested Citation: Suggested Citation