Conditional density forecasting: A tempered importance sampling approach

This paper proposes a new and robust methodology to obtain conditional density forecasts, based on information not contained in an initial econometric model. The methodology allows to condition on expected marginal densities for a selection of variables in the model, rather than just on future paths as it is usually done in the conditional forecasting literature. The proposed algorithm, which is based on tempered importance sampling, adapts the model-based density forecasts to target distributions the researcher has access to. As an example, this paper shows how to implement the algorithm by conditioning the forecasting densities of a BVAR and a DSGE model on information about the marginal densities of future oil prices. The results show that increased asymmetric upside risks to oil prices result in upside risks to inflation as well as higher core-inflation over the considered forecasting horizon. Finally, a real-time forecasting exercise yields that introducing market-based information on the oil price improves inflation and GDP forecasts during crises times such as the COVID pandemic.