The paper examines why U.S. inflation has become harder to forecast. It finds that the univariate inflation process is well described by a time-varying trend-cycle model with stochastic volatility or an integrated moving average (IMA) process with time-varying parameters. This model explains recent forecasting puzzles and suggests that multivariate forecasts do not consistently outperform univariate models. The paper analyzes changes in the inflation process since the mid-1950s, noting that the variance of the permanent disturbance has changed significantly, while the transitory disturbance has remained stable. The IMA(1,1) model, which is equivalent to the trend-cycle model, shows that the MA coefficient has increased over time, from approximately 0.25 in the 1970s to 0.65 in the 1984-2004 period. The paper also finds that the performance of the AO forecast has deteriorated since the mid-1980s, but it still performs well at long horizons. The paper concludes that the inflation process has changed, and fixed-parameter models like AO and Nelson-Schwert may not be effective in the future. Instead, time-varying models, such as the UC-SV model with stochastic volatility, or rolling IMA(1,1) models, may be more effective. The paper also finds that the performance of the NS77 model is good in the post-1984 period. Overall, the paper suggests that the inflation process has become more complex, and forecasting models need to adapt to these changes.The paper examines why U.S. inflation has become harder to forecast. It finds that the univariate inflation process is well described by a time-varying trend-cycle model with stochastic volatility or an integrated moving average (IMA) process with time-varying parameters. This model explains recent forecasting puzzles and suggests that multivariate forecasts do not consistently outperform univariate models. The paper analyzes changes in the inflation process since the mid-1950s, noting that the variance of the permanent disturbance has changed significantly, while the transitory disturbance has remained stable. The IMA(1,1) model, which is equivalent to the trend-cycle model, shows that the MA coefficient has increased over time, from approximately 0.25 in the 1970s to 0.65 in the 1984-2004 period. The paper also finds that the performance of the AO forecast has deteriorated since the mid-1980s, but it still performs well at long horizons. The paper concludes that the inflation process has changed, and fixed-parameter models like AO and Nelson-Schwert may not be effective in the future. Instead, time-varying models, such as the UC-SV model with stochastic volatility, or rolling IMA(1,1) models, may be more effective. The paper also finds that the performance of the NS77 model is good in the post-1984 period. Overall, the paper suggests that the inflation process has become more complex, and forecasting models need to adapt to these changes.