This paper investigates forecast aggregation via the random subspace regressions method (RSM) and explores the potential link between RSM and the Shapley value decomposition (SVD) using the US GDP growth rates. This technique combination enables handling high-dimensional data and reveals the relative importance of each individual forecast. First, it is possible to enhance forecasting performance in certain practical instances by randomly selecting smaller subsets of individual forecasts and obtaining a new set of predictions based on a regression-based weighting scheme. The optimal value of selected individual forecasts is also empirically studied. Then, a connection between RSM and SVD is proposed, enabling the examination of each individual forecast’s contribution to the final prediction, even when there is a large number of forecasts. This approach is model-agnostic (can be applied to any set of predictions) and facilitates understanding of how the aggregated prediction is obtained based on individual forecasts, which is crucial for decision-makers.

The substantial fluctuations in oil prices in the wake of the COVID-19 pandemic and the Russian invasion of Ukraine have highlighted the importance of tail events in the global market for crude oil which call for careful risk assessment. In this paper we focus on forecasting tail risks in the oil market by setting up a general empirical framework that allows for flexible predictive distributions of oil prices that can depart from normality. This model, based on Bayesian additive regression trees, remains agnostic on the functional form of the conditional mean relations and assumes that the shocks are driven by a stochastic volatility model. We show that our nonparametric approach improves in terms of tail forecasts upon three competing models: quantile regressions commonly used for studying tail events, the Bayesian VAR with stochastic volatility, and the simple random walk. We illustrate the practical relevance of our new approach by tracking the evolution of predictive densities during three recent economic and geopolitical crisis episodes, by developing consumer and producer distress indices that signal the build-up of upside and downside price risk, and by conducting a risk scenario analysis for 2024.