Forecasting inflation is an important and challenging task. In this paper we assume that the core inflation components evolve as a multivariate local level process. This model, which is theoretically attractive for modelling inflation dynamics, has been used only to a limited extent to date owing to computational complications with the conventional multivariate maximum likelihood estimator, especially when the system is large. We propose the use of a method called "Moments Estimation Through Aggregation" (M.E.T.A.), which reduces computational costs significantly and delivers prompt and accurate parameter estimates, as we show in a Monte Carlo exercise. In an application to euro-area inflation we find that our forecasts compare well with those generated by alternative univariate constant and timevarying parameter models as well as with those of professional forecasters and vector autoregressions.JEL Classification: C32, C53, E31, E37.