On Adjusting the One-Sided Hodrick-Prescott Filter
19 Pages Posted: 27 Mar 2020
Date Written: January 21, 2020
We show that one should not use the one-sided Hodrick-Prescott filter (HP-1s) as the real-time version of the two-sided Hodrick-Prescott filter (HP-2s): First, in terms of the extracted cyclical component, HP-1s fails to remove low-frequency fluctuations to the same extent as HP-2s. Second, HP-1s dampens fluctuations at all frequencies -- even those it is meant to extract. As a remedy, we propose two small adjustments to HP-1s, aligning its properties closely with HP-2s: (1) a lower value for the smoothing parameter and (2) a multiplicative rescaling of the extracted cyclical component. For example, for HP-2s with lambda = 1,600 (value of smoothing parameter), the adjusted one-sided HP filter uses lambda_star = 650 and rescales the extracted cyclical component by a factor of 1.1513. Using simulated and empirical data, we illustrate the relevance of the adjustments. For instance, financial cycles may appear 1.7 times more volatile than business cycles, where in fact volatilities differ only marginally.
Keywords: Real-time analysis, detrending, business cycles, financial cycles
JEL Classification: C10, E32, E58, G01
Suggested Citation: Suggested Citation