Comparing density forecasts of aggregated time series via bootstrap

When forecasting aggregated time series, several options are available. For example, the multivariate series or the individual time series might be predicted and then aggregated, or one may choose to forecast the aggregated series directly. While in theory an optimal disaggregated forecast will generally be superior (or at least not inferior) to forecasts based on aggregated information, this is not necessarily true in practical situations. The main reason is that the true data generating process is usually unknown and models need to be specified and estimated on the basis of the available information. This paper describes a bootstrap-based procedure, in the context of vector autoregressive models, for ranking the different forecasting approaches for contemporaneous time series aggregates. Estimation uncertainty and model misspecification will be considered and the ranking will be based not only on the mean squared forecast error, but more in general on the performance of the predictive distribution. The forecasting procedures are applied to the United States aggregate inflation.