In this article, it is analysed the multihorizon predictive power of the Hybrid New Keynesian Phillips Curve (HNKPC) making use of a compact-scale Global VAR for the headline inflation of six developed countries with different inflationary experiences; covering from 2000.1 until 2014.12. The key element of this article is the use of direct measures of inflation expectations--Consensus Economics--embedded in a Global VAR environment, i.e. modelling cross-country interactions. The Global VAR point forecast is evaluated using the Mean Squared Forecast Error (MSFE) statistic and statistically compared with several benchmarks. These belong to traditional statistical modelling, such as autoregressions (AR), the exponential smoothing model (ES), and the random walk model (RW). One last economics-based benchmark is the closed economy univariate HNKPC. The results indicate that the Global VAR is a valid forecasting procedure especially for the short-run. The most accurate forecasts, however, are obtained with the AR and especially with the univariate HNKPC. In the long-run, the ES model also appears as a better alternative rather than the RW. The MSPE is obviously affected by the unanticipated effects of the financial crisis started in 2008. So, when considering an evaluation sample just before the crisis, the GVAR also appears as a valid alternative in the long-run. The most robust forecasting devices across countries and horizons result in the univariate HNKPC, giving a role for economic fundamentals when forecasting inflation.