Suppose we are interested in forecasting a time series and, in addition to the time series data, we have data from many time series related to the one we want to forecast. Since building a dynamic multivariate model for the set of time series can be a complex task, it is important to measure in advance the increase in precision to be attained by using multivariate forecasts with respect to univariate ones. This article presents a simple procedure designed to obtain a consistent estimate of this measure. Its performance is illustrated with Monte Carlo simulations and examples. © 2007 Blackwell Publishing Ltd.