We propose a noncausal autoregressive model with time-varying parameters, and apply it to U.S. postwar inflation. The model .fits the data well, and the results suggest that inflation persistence follows from future expectations. Persistence has declined in the early 1980.s and slightly increased again in the late 1990.s. Estimates of the new Keynesian Phillips curve indicate that current inflation also depends on past inflation although future expectations dominate. The implied trend inflation estimate evolves smoothly and is well aligned with survey expectations. There is evidence in favor of the variation of trend inflation following from the underlying marginal cost that drives inflation.