We examine recursive out-of-sample forecasting of monthly postwar US core inflation and log price levels. We use the autoregressive fractionally integrated moving average model with explanatory variables (ARFIMAX). Our analysis suggests a significant explanatory power of leading indicators associated with macroeconomic activity and monetary conditions for forecasting horizons up to 2 years. Correcting for the effect of explanatory variables, we still find fractional integration and structural breaks in the mean and variance of inflation in the 1970s and 1980s. We compare the forecasts of ARFIMAX models and ARIMAX models over the period 1984-1999. The ARIMAX (1, 1, 1) model provides the best forecasts, but its multi-step forecast intervals are too large. The multi-step forecast intervals of the ARFIMAX(0, d, 0) model prove to be more realistic. © 2002 International Institute of Forecasters. Published by Elsevier Science B.V. All rights reserved.