Combining density forecast accuracy tests: an application to agricultural, energy, and metal commodities

Abstract This study develops a new methodology for combining density forecast accuracy tests and assessing the relevance of psychological indicators in predicting commodity returns. Density forecasts provide a complete description of the uncertainty associated with a prediction and are highly requested by policymakers, central bankers, and financial operators to define policy actions, manage financial risks, and assess portfolio selection. The proposed methodology combines different tests and derives the p-value of the resulting test statistic by Monte Carlo simulations. To assess the power of the proposed methodology, we implement a set of experiments for several data-generating processes. Based on an empirical forecasting exercise applied to agricultural, energy, and metal commodities, we find that sentiment variables and psychological factors improve the density forecasts of commodity futures returns, especially for agricultural commodities. Additionally, combinations of sentiment variables are more powerful in predicting returns than considering them separately.