Policymakers and researchers see ination characterized by cyclical uctuations driven by changes in resource utilization and temporary shocks, around a trend inuenced by ination expectations. We study the in-sample ination dynamics and forecast ination outof-sample by analyzing a New Keynesian Phillips Curve (NKPC) in the frequency domain.In-sample, while ination expectations dominate medium-to-long-run cycles, energy prices dominate short cycles and business-to-medium cycles once expectations became anchored.While statistically signicant, unemployment is not economically relevant for any cycle. Outof-sample, forecasts from a low-frequency NKPC signicantly outperform several benchmark models. The long-run component of unemployment is key for such remarkable forecasting performance.