On Adjusting the One-Sided Hodrick-Prescott Filter
30 Pages Posted: 27 Mar 2020 Last revised: 7 Mar 2022
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 those of 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* = 650 and rescales the extracted cyclical component by a factor of 1:1513. Using simulated and empirical data, we illustrate the relevance of these adjustments. For instance, financial cycles may appear to be 70% 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