Regularizing Bayesian Predictive Regressions

35 Pages Posted: 17 Aug 2016 Last revised: 25 Oct 2021

See all articles by Guanhao Feng

Guanhao Feng

City University of Hong Kong (CityU)

Nick Polson

University of Chicago - Booth School of Business

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

Feng, Guanhao and Polson, Nick, Regularizing Bayesian Predictive Regressions (June 6, 2016). Available at SSRN: or

Guanhao Feng (Contact Author)

City University of Hong Kong (CityU) ( email )

83 Tat Chee Avenue
Kowloon Tong
Hong Kong

Nick Polson

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-702-7513 (Phone)
773-702-0458 (Fax)

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