We evaluate the ability of several univariate models to predict inflation in the US and in a number of inflation targeting countries at different forecasting horizons. We focus on forecasts coming from a family of ten seasonal models that we call the Driftless Extended Seasonal ARIMA (DESARIMA) family. Using out-of-sample Root Mean Squared Prediction Errors (RMSPE) we compare the forecasting accuracy of the DESARIMA family with that of traditional univariate time-series benchmarks available in the literature. Our results show that DESARIMA-based forecasts display lower RMSPE at short horizons for every single country, with the exception of one case. We obtain mixed results at longer horizons. In particular, when the family-median forecast is considered, in more than half of the countries our DESARIMA-based forecasts outperform the benchmarks at long horizons. Remarkably, the forecasting accuracy of our DESARIMA family is high in stable-inflation countries, for which the RMSPE is around 100 basis points when a prediction is made 24 and even 36 months ahead.