Hodrick-Prescott Filter: Trend-Cycle Decomposition for Macroeconomic Time Series

The Hodrick-Prescott (HP) filter is a penalized least-squares technique used in macroeconomics and empirical finance to decompose a time series into a smooth long-run trend component and a short-run cyclical component. Introduced by Hodrick and Prescott (1997) using postwar U.S. business cycle data, it has become one of the most widely applied filters in business cycle analysis, monetary policy research, and applied econometrics.