Bayesian model averaging and the conditional volatility process: an application to predicting aggregate equity returns by conditioning on economic variables

Abstract

This study revisits the topic of predicting aggregate equity returns out-of-sample by conditioning on economic variables through Bayesian model averaging (BMA). Besides simultaneously addressing parameter instability and model uncertainty, I suggest a new model feature, namely, predictors in a given model can also impact the dependent variable through the conditional volatility process. The suggested econometric framework is straightforward to implement without requiring simulation. Likewise, the user can easily decide, which aspects of the predictive channel should to be switched on, off or altered. I apply the suggested framework to the well-known [Goyal, A. and Welch, I., A comprehensive look at the empirical performance of equity premium prediction. Rev. Financial Stud., 2008, 21, 1455–1508] dataset. An extensive out-of-sample prediction evaluation demonstrates that averaging over predictor combinations in a model that allows lagged predictors to impact aggregate equity returns exclusively through the conditional volatility process results in statistically significant more accurate density predictions relative to the benchmark, especially when predicting the left tail of the conditional distribution. One also observes economic gains in favor of certain BMAs. Here, the BMA that allows predictors to impact equity returns through the conditional mean as well as the conditional volatility process is the top performer.