Modeling the out-of-sample predictive relationship between equity premium, returns on the price of crude oil and economic policy uncertainty using multivariate time-varying dimension models

Researchers increasingly rely on the newspaper-based uncertainty (volatility) measures pioneered by Baker et al. (2016) to forecast economic, financial variables and commodity prices out-of-sample. Among them, equity premium and returns on the price of crude oil have received a great deal of attention given their importance. By combining different linear state-space representations of the multivariate dynamic linear model with the discount factor-based model averaging (selection) technique outlined in Raftery et al. (2010), and using monthly data from 1997m1 through 2022m10, we suggest three multivariate time-varying dimension models, and forecast these variables out-of-sample in a contemporaneous fashion. The time-varying dimension feature allows the number of predictors in each regression of the multivariate system to change over time. From a technical viewpoint, the suggested models are intuitive (flexible), and do not require much subjective input from the researcher. They also produce very accurate one-month ahead out-of-sample density (point) forecasts on average. From an empirical viewpoint, our analysis provides new and interesting insights into the out-of-sample predictive relationship between equity premium, returns on the price of crude oil and economic policy uncertainty.