Low frequency filtering and real business cycles

This paper discusses in detail the Hodrick-Prescott (1980) filter from time and frequency domain perspectives, motivating it as a generalization of the exponential smoothing filter. We show that the HP filter — when applied to large samples — contains a centered fourth difference and hence renders stationary time series that are ‘difference-stationary’ and, indeed, integrated of higher order. However, our application of the HP filter to U.S. time series and to the simulated outcomes of real business cycle models leads us to question its widespread use as a unique method of trend elimination. We provide examples of how HP filtering dramatically alters measures of persistence, variability, and comovement.