The paper examines the changing nature of U.S. inflation forecasting, noting that while inflation has become easier to forecast in terms of reduced forecast errors, the relative performance of standard multivariate models has deteriorated since the mid-1980s. The authors propose a model that describes the univariate inflation process as a combination of a permanent stochastic trend and a serially uncorrelated transitory component, with the variance of the permanent component changing over time. This model explains the historical performance of univariate inflation forecasts and suggests that the shift in forecasting performance is due to changes in the inflation process. The paper also discusses the implications of these findings for multivariate Phillips curve forecasts and proposes two approaches for real-time univariate forecasting: an unobserved components model with stochastic volatility and an IMA(1,1) model with time-varying parameters.The paper examines the changing nature of U.S. inflation forecasting, noting that while inflation has become easier to forecast in terms of reduced forecast errors, the relative performance of standard multivariate models has deteriorated since the mid-1980s. The authors propose a model that describes the univariate inflation process as a combination of a permanent stochastic trend and a serially uncorrelated transitory component, with the variance of the permanent component changing over time. This model explains the historical performance of univariate inflation forecasts and suggests that the shift in forecasting performance is due to changes in the inflation process. The paper also discusses the implications of these findings for multivariate Phillips curve forecasts and proposes two approaches for real-time univariate forecasting: an unobserved components model with stochastic volatility and an IMA(1,1) model with time-varying parameters.