A stylized fact of U.S. inflation dynamics is one of extreme persistence and possible unit root behavior. If so, the implications for macroeconomics and monetary policy are somewhat unpalatable. Our econometric analysis proposes a parsimonious univariate representation of the inflation process for the last 60 years, the nonlinear exponential smooth autoregressive. The empirical results confirm a number of the key features such as global stationarity, local unit root behavior, and lower persistence in the post-1983 period than in the pre-1983 period. We compare the forecasting ability of our model with that of competing univariate models and find that the nonlinear model outperforms the linear autoregressive model in the pre-1983 period and the random walk in the post-1983 period at short horizons.